4. Name a big idea (major concept) in your subject area and write a one paragraph rationale for why students should learn it.

4. Name a big idea (major concept) in your subject area and write a one paragraph rationale for why students should learn it.

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EE118 FALL 2012 SAN JOSE STATE UNIVERSITY Department of Electrical Engineering TEST 2 — Digital Design I October 24, 2012 10:30 a.m. – 11:45 a.m. — Closed Book & Closed Notes — — No Crib Sheet Allowed — STUDENT NAME: (Last) Claussen , (First) Matthew STUDENT ID NUMBER (LAST 4 DIGITS): No interpretation of test problems will be given during the test. If you are not sure of what is intended, make appropriate assumptions and continue. Do not unstaple !!! Problems 1-14(4 points each) TOTAL Problems 15 – 17 (15 pts each) 1203 2 For the next 14 problems, circle the correct answer. No partial credit will be given. PROBLEM 1 (4 points) Which statement is not true? A. Any combinational circuit may be designed using multiplexers only. B. Any combinational circuit may be designed using decoders only. C. All Sequential circuits are based on cross-coupled NAND or NOR gates. D. A hazard in a digital system is an undesirable effect caused by either a deficiency in the system or external influences. E. None of the above PROBLEM 2 (4 points) For a 2-bit comparator comparing 2-bit numbers A = (a1 a0) and B = (b1 b0), what is the proper function for the f(A>B) output through logical reasoning? A. a1 b1’ + (a1 b1 + a1’b1’ ) a0 b0’ B. a1 b1’ + (a1 b1’+ a1’b1 ) a0 b0 C. a1 a0’ + (a1 a0 + b1’b0’ ) b1 b0’ D. a1 a0 + (a1 a0’+ b1’b0 ) b1 b0 PROBLEM 3 (4 points) What is the priority scheme of this encoder? Inputs Outputs I3 I2 I1 I0 O1 O 0 d d 1 d 0 1 d d 0 1 0 0 d 1 0 0 1 0 1 0 0 0 1 1 A. I3 > I2 > I1 >I0 B. I0 > I1 > I2 >I3 C. I1 > I0 > I2 >I3 D. I2 > I1 > I3 >I0 3 PROBLEM 4 (4 points) Which is the correct binary representation of the decimal number 46.625? A. 101101.001 B. 101000.01 C. 111001.001 D. 101110.101 PROBLEM 5 (4 points) Which is the decimal equivalent number of the sum of the two 8-bit 2’s complement numbers FB16 and 3748? A. 3 B. 5 C. 7 D. 9 PROBLEM 6 (4 points) For the MUX-based circuit shown below, f(X,Y,Z) = ? X Y Z f A. X’Y’ + Y’Z’ B. X’Y’Z’ + YZ’ C. XYZ’ + Y’Z D. X’Y’Z’ + YZ 1 0 MUX 4 PROBLEM 7 (4 points) Which is the correct output F of this circuit? E C B D F A A. (A’E+AB)(C’D) B. (AE+A’B)(C’+D) C. (A’E+AB)(C’D’+CD’+CD) D. (A’E+AB)(CD’)’ PROBLEM 8 (5 points) In order to correctly perform 2910  14510, how many bits are required to represent the numbers? A 8 B 9 C 10 D 11 PROBLEM 9 (4 points) Which is the negative 2’s complement equivalent of the 8-bit number 01001101? A. 11001101 B. 10111100 C. 10110000 D. 10110011 0 2-1 1 MUX 0 0 1 1 2-4 decoder 2 EN 3 5 PROBLEM 10 (4 points) Which is the correct statement describing the behavior of the following Verilog code? module whatisthis(hmm, X, Y); output [3:0] hmm; input [3:0] X, Y; assign hmm = (X < Y) ? X : Y; endmodule A. If X>Y, hmm becomes 1111. B. hmm assumes min(X,Y). C. If X<Y, hmm becomes 1111. D. hmm assumes max(X,Y). PROBLEM 11 (4 points) Which Boolean expression corresponds to the function g(W,X,Y,Z) implemented by the following “non-priority” encoder-based circuit? Assume that one and only one input is high at any time. f W X g Y Z A. Y + Z B. W + Y C. X + Y D. X + Z PROBLEM 12 (4 points) Which Boolean expression corresponds to the output of the following logic diagram? (/B = B’) A. Z = ( A(B’ + C)’ )’ + ( (B’ + C)’ + D )’ B. Z= A(B C’) + (B C’ + D) C. Z = (A(B’ + C)(B’ + C + D) )’ D. Z = A(B’ + C)’ + (B’ + C + D)’ 0 0 1 1 2 3 Encoder 6 PROBLEM 13 (4 points) Which is the correct gate-level circuit in minimal SOP form for the following circuit? A F = Y’X’ + W’ZY’X B F = YX’ + W’Z’Y’X C F = YX’ + W’ZY’X D F = Y’X + W’ZY’X’ PROBLEM 14 (4 points) For the following flow map of a certain cross-coupled gate circuit, the circuit is currently in the underlined state. If the inputs YZ change to 11, the circuit becomes meta-stable. Between which two states (WX) does the circuit oscillate ? A 00  11 B 01  10 C 11  10 D 10  00 YZ WX 00 01 11 10 00 00 11 00 10 01 10 10 10 01 11 00 00 11 01 10 10 01 01 10 G1 Y0 G2A Y1 G2B Y2 Y3 A Y4 B Y5 C Y6 Y7 G1 Y0 G2A Y1 G2B Y2 Y3 A Y4 B Y5 C Y6 Y7 OR W X Y Z X Y Z F + 5 V 7 For each of the next 3 problems, show all your work. Partial credits will be given. PROBLEM 15 (15 points) 1) Which logic variable causes the hazard for the circuit given by the K-map below? 2) Using the timing diagram, clearly show how the hazard occurs. 3) Find the best hazard-free logic function. YZ WX 00 01 11 10 00 0 0 1 1 01 0 0 0 0 11 1 0 0 0 10 1 0 1 1 8 PROBLEM 16(15 points) Analyze the following cross-coupled NAND gates by showing: (a) flow map with stable states circled and with meta-stability condition shown by arrows, (b) state table, and (c) completed timing diagram below. Note that d is the propagation delay of each gate. XY G1(t)G2(t) 00 01 11 10 00 01 11 10 Inputs  XY=00 XY=01 XY=11 XY=10 Present States  X Y G1(t) G2(t) 0 d 2d 3d 4d 5d 6d 7d 8d 9d X Y G1 G2 9 PROBLEM 17 (15 points) Using Quine-McCluskey algorithm, find the minimal SOP for the following minterm list. f(A, B, C) = (1,2,3,4,6,7) w(j) j Match I Match II 0 1 2 3 PI Covering Table

EE118 FALL 2012 SAN JOSE STATE UNIVERSITY Department of Electrical Engineering TEST 2 — Digital Design I October 24, 2012 10:30 a.m. – 11:45 a.m. — Closed Book & Closed Notes — — No Crib Sheet Allowed — STUDENT NAME: (Last) Claussen , (First) Matthew STUDENT ID NUMBER (LAST 4 DIGITS): No interpretation of test problems will be given during the test. If you are not sure of what is intended, make appropriate assumptions and continue. Do not unstaple !!! Problems 1-14(4 points each) TOTAL Problems 15 – 17 (15 pts each) 1203 2 For the next 14 problems, circle the correct answer. No partial credit will be given. PROBLEM 1 (4 points) Which statement is not true? A. Any combinational circuit may be designed using multiplexers only. B. Any combinational circuit may be designed using decoders only. C. All Sequential circuits are based on cross-coupled NAND or NOR gates. D. A hazard in a digital system is an undesirable effect caused by either a deficiency in the system or external influences. E. None of the above PROBLEM 2 (4 points) For a 2-bit comparator comparing 2-bit numbers A = (a1 a0) and B = (b1 b0), what is the proper function for the f(A>B) output through logical reasoning? A. a1 b1’ + (a1 b1 + a1’b1’ ) a0 b0’ B. a1 b1’ + (a1 b1’+ a1’b1 ) a0 b0 C. a1 a0’ + (a1 a0 + b1’b0’ ) b1 b0’ D. a1 a0 + (a1 a0’+ b1’b0 ) b1 b0 PROBLEM 3 (4 points) What is the priority scheme of this encoder? Inputs Outputs I3 I2 I1 I0 O1 O 0 d d 1 d 0 1 d d 0 1 0 0 d 1 0 0 1 0 1 0 0 0 1 1 A. I3 > I2 > I1 >I0 B. I0 > I1 > I2 >I3 C. I1 > I0 > I2 >I3 D. I2 > I1 > I3 >I0 3 PROBLEM 4 (4 points) Which is the correct binary representation of the decimal number 46.625? A. 101101.001 B. 101000.01 C. 111001.001 D. 101110.101 PROBLEM 5 (4 points) Which is the decimal equivalent number of the sum of the two 8-bit 2’s complement numbers FB16 and 3748? A. 3 B. 5 C. 7 D. 9 PROBLEM 6 (4 points) For the MUX-based circuit shown below, f(X,Y,Z) = ? X Y Z f A. X’Y’ + Y’Z’ B. X’Y’Z’ + YZ’ C. XYZ’ + Y’Z D. X’Y’Z’ + YZ 1 0 MUX 4 PROBLEM 7 (4 points) Which is the correct output F of this circuit? E C B D F A A. (A’E+AB)(C’D) B. (AE+A’B)(C’+D) C. (A’E+AB)(C’D’+CD’+CD) D. (A’E+AB)(CD’)’ PROBLEM 8 (5 points) In order to correctly perform 2910  14510, how many bits are required to represent the numbers? A 8 B 9 C 10 D 11 PROBLEM 9 (4 points) Which is the negative 2’s complement equivalent of the 8-bit number 01001101? A. 11001101 B. 10111100 C. 10110000 D. 10110011 0 2-1 1 MUX 0 0 1 1 2-4 decoder 2 EN 3 5 PROBLEM 10 (4 points) Which is the correct statement describing the behavior of the following Verilog code? module whatisthis(hmm, X, Y); output [3:0] hmm; input [3:0] X, Y; assign hmm = (X < Y) ? X : Y; endmodule A. If X>Y, hmm becomes 1111. B. hmm assumes min(X,Y). C. If X

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Question 1 1. When the rules of perspective are applied in order to represent unusual points of view, we call this ________. a. foreshortening b. chiaroscuro c. convergence d. highlight e. overlapping 10 points Question 2 1. A flat work of art has two dimensions: ________ and width. a. breadth b. depth c. size d. mass e. height 10 points Question 3 1. Méret Oppenheim was part of an art movement that rejected rational, conscious thought. Her fur-lined teacup and saucer, Object, conjures an unexpected and illogical sensation for the viewer by using ________ texture. a. smooth b. familiar c. expected d. subversive e. silky 10 points Question 4 1. In James Allen’s etching The Connectors, an image of workers erecting the Empire State Building, the artist created a feeling of great height by using ________ line to lead the viewer’s eye diagonally downward. a. horizontal b. communicative c. regular d. directional e. implied 10 points Question 5 1. Because it is three-dimensional, a form has these three spatial measurements: height, width, and ________. a. mass b. length c. size d. depth e. strength 10 points Question 6 1. The ancient Egyptian depiction of the journey of the Sun god Re (0.1) was painted on ________. a. stone b. a coffin c. the wall of a tomb d. copper e. a vase 10 points Question 7 1. The area covered by a pattern is called the ________. a. field b. motif c. background d. size e. foreground 10 points Question 8 1. ________ balance is achieved when two halves of a composition are not mirror images of each other. a. unified b. radial c. varied d. asymmetrical e. symmetrical 10 points Question 9 1. In Audrey Flack’s Marilyn Monroe, the burning candle, the flower, and the hourglass are typical of a kind of symbolism in art that reminds us of death. This kind of symbolism is known as ________. a. vanitas b. feminism c. abstract d. eternal e. none of the other answers 10 points Question 10 1. Tibetan Buddhist monks create colored sand images with a radial design. This representation of the universe is called a ________. a. prayer wheel b. rotunda c. mandala d. prayer flag e. lotus 10 points Question 11 1. In The School of Athens, Raphael focused our attention on two Greek philosophers positioned in the center of the work. They are ________ and ________. a. Plato . . . Aristotle b. Aristotle . . . Socrates c. Diogenes . . . Socrates d. Diogenes . . . Aristotle e. Socrates . . . Plato 10 points Question 12 1. In his Obey campaign poster Shepard Fairey used a striking contrast between positive and ________ shapes to attract the attention of the public. a. figure–ground reversal b. implied c. geometric d. organic e. negative 10 points Question 13 1. The Italian architect Andrea Palladio created a radial design in his plan for the Villa Capra. This building is also called the ________. a. Colosseum b. Pantheon c. Villa Rotonda d. Villa Caprese e. Parthenon 10 points Question 14 1. The French artist Georges Seurat employed a new technique to create a jewel-like diffusion of light and vibration of color in his work The Circus. This type of painting, made up of small dots of color, is known as ________. a. Fauvism b. Luminism c. pointillism d. Pop art e. Impressionism 10 points Question 15 1. The rarity of an artwork, and its value, are often closely related. True False 10 points Question 16 1. By orienting lines so that they attract attention to a specific area of a work of art the artist is using ________. a. actual line b. implied line c. directional line d. measured line e. chaotic line 10 points Question 17 1. Kindred Spirits by Asher Brown Durand uses the effects of ________ to give a sense of the vastness of the American landscape. a. pencil drawing b. geometry c. atmospheric perspective d. foreshortening e. color 10 points Question 18 1. The opposite of emphasis is ________. a. subordination b. tone c. focal point d. color e. proportion 10 points Question 19 1. Gustav Klimt’s portrait of Adele Bloch-Bauer was typical of his portraits of the wives and sisters of ________. a. foreign tourists b. Nazi rulers c. German scientists d. Austrian businessmen e. important politicians 10 points Question 20 1. The combination of jarring vertical and diagonal lines in Vincent van Gogh’s The Bedroom creates an atmosphere of ________. a. happiness b. rest c. anxiety d. expectation e. calm 10 points Question 21 1. If the clothing of the saint was the only light area in The Funeral of St. Bonaventure, the viewer’s eye would not be easily drawn to any other areas of the composition. True False 10 points Question 22 1. Miriam Schapiro’s collage Baby Blocks combines two different kinds of shape. ________ is the term used to describe a shape that suggests the natural world, while the term geometric suggests mathematical regularity. a. conceptual b. implied c. organic d. regular e. artificial 10 points Question 23 1. Any of the ________ of art can help focus our interest on specific areas of a work of art. a. styles b. elements c. periods d. tones e. themes 10 points Question 24 1. An artwork can be described as non-objective if its subject matter is ________. a. three-dimensional b. difficult c. unrecognizable d. recognizable e. animals 10 points Question 25 1. Match the methodological approach with its definition: biographical analysis feminist analysis formal analysis contextual analysis 2. iconographical analysis a. analyzes the use of formal elements in a work. b. considers the role of women in an artwork c. interprets objects and figures in the artwork as symbols d. considers the artist’s personal experiences e. considers the religious, political, and social environment in which the artwork was made and viewed 10 points Question 26 1. Alexander Calder invented the ________, a type of suspended, balanced sculpture that uses air currents to power its movement. a. mime b. relief c. mobile d. stabile e. zoetrope 10 points Question 27 1. Louise Nevelson’s work White Vertical Water is a realistic depiction of fish in a river. True False 10 points Question 28 1. William G. Wall’s Fort Edward was published as a ________. a. print b. watercolor c. photograph d. oil painting e. newspaper article 10 points Question 29 1. Artemisia Gentileschi worked during this stylistic and historical period. a. Surrealism b. Impressionism c. Baroque d. Renaissance e. Pop art 10 points Question 30 1. The process of using a series of parallel lines set close to one another to differentiate planes of value in a work of art is called ________. a. highlight b. core shadow c. perspective d. hatching e. palette 10 points Question 31 1. The artist Canaletto, in his drawing of the Ducal Palace in Venice, created an impression of three dimensions by using line to show the division between ________. a. planes b. two figures c. colors d. time periods e. mountains 10 points Question 32 1. Marisol’s work Father Damien was created to memorialize the heroism of a priest who lost his life helping the victims of leprosy. This sculpture stands in front of the State Capitol Building in the U.S. State of ________. a. Arizona b. Pennsylvania c. Utah d. Tennessee e. Hawaii 10 points Question 33 1. The medium of Marc Quinn’s Self is: a. clay b. the artist’s toenail clippings c. wood d. real human hair e. the artist’s own blood 10 points Question 34 1. The work now known as the Watts Towers was in fact given a different title by its creator. That title was ________. a. Nuestro Pueblo b. LA Towers c. Found Objects d. it had no title originally e. Skyscrapers 1 and 2 10 points Question 35 1. Why do we presume that the head of a woman from Benin (0.18) was made for someone wealthy? a. because it was made to be shown in a museum b. because it strongly resembles the Queen c. because it has a price carved on the back d. because it was made from rare ivory e. it was definitely not made for anyone wealthy 10 points Question 36 1. Shahzia Sikander’s art is best described as Abstract Expressionism Naturalist sculpture Pop Art Miniature Painting 10 points Question 37 1. A sunset is a work of art. True False 10 points Question 38 1. A mens’ urinal became a well known artwork in the 20th century. True False 10 points Question 39 1. Which artist has torn out people’s lawns to design and build edible gardens across the country? Andrea Zittel Fritz Haeg Ruben Ortiz Torres Mark Newport

Question 1 1. When the rules of perspective are applied in order to represent unusual points of view, we call this ________. a. foreshortening b. chiaroscuro c. convergence d. highlight e. overlapping 10 points Question 2 1. A flat work of art has two dimensions: ________ and width. a. breadth b. depth c. size d. mass e. height 10 points Question 3 1. Méret Oppenheim was part of an art movement that rejected rational, conscious thought. Her fur-lined teacup and saucer, Object, conjures an unexpected and illogical sensation for the viewer by using ________ texture. a. smooth b. familiar c. expected d. subversive e. silky 10 points Question 4 1. In James Allen’s etching The Connectors, an image of workers erecting the Empire State Building, the artist created a feeling of great height by using ________ line to lead the viewer’s eye diagonally downward. a. horizontal b. communicative c. regular d. directional e. implied 10 points Question 5 1. Because it is three-dimensional, a form has these three spatial measurements: height, width, and ________. a. mass b. length c. size d. depth e. strength 10 points Question 6 1. The ancient Egyptian depiction of the journey of the Sun god Re (0.1) was painted on ________. a. stone b. a coffin c. the wall of a tomb d. copper e. a vase 10 points Question 7 1. The area covered by a pattern is called the ________. a. field b. motif c. background d. size e. foreground 10 points Question 8 1. ________ balance is achieved when two halves of a composition are not mirror images of each other. a. unified b. radial c. varied d. asymmetrical e. symmetrical 10 points Question 9 1. In Audrey Flack’s Marilyn Monroe, the burning candle, the flower, and the hourglass are typical of a kind of symbolism in art that reminds us of death. This kind of symbolism is known as ________. a. vanitas b. feminism c. abstract d. eternal e. none of the other answers 10 points Question 10 1. Tibetan Buddhist monks create colored sand images with a radial design. This representation of the universe is called a ________. a. prayer wheel b. rotunda c. mandala d. prayer flag e. lotus 10 points Question 11 1. In The School of Athens, Raphael focused our attention on two Greek philosophers positioned in the center of the work. They are ________ and ________. a. Plato . . . Aristotle b. Aristotle . . . Socrates c. Diogenes . . . Socrates d. Diogenes . . . Aristotle e. Socrates . . . Plato 10 points Question 12 1. In his Obey campaign poster Shepard Fairey used a striking contrast between positive and ________ shapes to attract the attention of the public. a. figure–ground reversal b. implied c. geometric d. organic e. negative 10 points Question 13 1. The Italian architect Andrea Palladio created a radial design in his plan for the Villa Capra. This building is also called the ________. a. Colosseum b. Pantheon c. Villa Rotonda d. Villa Caprese e. Parthenon 10 points Question 14 1. The French artist Georges Seurat employed a new technique to create a jewel-like diffusion of light and vibration of color in his work The Circus. This type of painting, made up of small dots of color, is known as ________. a. Fauvism b. Luminism c. pointillism d. Pop art e. Impressionism 10 points Question 15 1. The rarity of an artwork, and its value, are often closely related. True False 10 points Question 16 1. By orienting lines so that they attract attention to a specific area of a work of art the artist is using ________. a. actual line b. implied line c. directional line d. measured line e. chaotic line 10 points Question 17 1. Kindred Spirits by Asher Brown Durand uses the effects of ________ to give a sense of the vastness of the American landscape. a. pencil drawing b. geometry c. atmospheric perspective d. foreshortening e. color 10 points Question 18 1. The opposite of emphasis is ________. a. subordination b. tone c. focal point d. color e. proportion 10 points Question 19 1. Gustav Klimt’s portrait of Adele Bloch-Bauer was typical of his portraits of the wives and sisters of ________. a. foreign tourists b. Nazi rulers c. German scientists d. Austrian businessmen e. important politicians 10 points Question 20 1. The combination of jarring vertical and diagonal lines in Vincent van Gogh’s The Bedroom creates an atmosphere of ________. a. happiness b. rest c. anxiety d. expectation e. calm 10 points Question 21 1. If the clothing of the saint was the only light area in The Funeral of St. Bonaventure, the viewer’s eye would not be easily drawn to any other areas of the composition. True False 10 points Question 22 1. Miriam Schapiro’s collage Baby Blocks combines two different kinds of shape. ________ is the term used to describe a shape that suggests the natural world, while the term geometric suggests mathematical regularity. a. conceptual b. implied c. organic d. regular e. artificial 10 points Question 23 1. Any of the ________ of art can help focus our interest on specific areas of a work of art. a. styles b. elements c. periods d. tones e. themes 10 points Question 24 1. An artwork can be described as non-objective if its subject matter is ________. a. three-dimensional b. difficult c. unrecognizable d. recognizable e. animals 10 points Question 25 1. Match the methodological approach with its definition: biographical analysis feminist analysis formal analysis contextual analysis 2. iconographical analysis a. analyzes the use of formal elements in a work. b. considers the role of women in an artwork c. interprets objects and figures in the artwork as symbols d. considers the artist’s personal experiences e. considers the religious, political, and social environment in which the artwork was made and viewed 10 points Question 26 1. Alexander Calder invented the ________, a type of suspended, balanced sculpture that uses air currents to power its movement. a. mime b. relief c. mobile d. stabile e. zoetrope 10 points Question 27 1. Louise Nevelson’s work White Vertical Water is a realistic depiction of fish in a river. True False 10 points Question 28 1. William G. Wall’s Fort Edward was published as a ________. a. print b. watercolor c. photograph d. oil painting e. newspaper article 10 points Question 29 1. Artemisia Gentileschi worked during this stylistic and historical period. a. Surrealism b. Impressionism c. Baroque d. Renaissance e. Pop art 10 points Question 30 1. The process of using a series of parallel lines set close to one another to differentiate planes of value in a work of art is called ________. a. highlight b. core shadow c. perspective d. hatching e. palette 10 points Question 31 1. The artist Canaletto, in his drawing of the Ducal Palace in Venice, created an impression of three dimensions by using line to show the division between ________. a. planes b. two figures c. colors d. time periods e. mountains 10 points Question 32 1. Marisol’s work Father Damien was created to memorialize the heroism of a priest who lost his life helping the victims of leprosy. This sculpture stands in front of the State Capitol Building in the U.S. State of ________. a. Arizona b. Pennsylvania c. Utah d. Tennessee e. Hawaii 10 points Question 33 1. The medium of Marc Quinn’s Self is: a. clay b. the artist’s toenail clippings c. wood d. real human hair e. the artist’s own blood 10 points Question 34 1. The work now known as the Watts Towers was in fact given a different title by its creator. That title was ________. a. Nuestro Pueblo b. LA Towers c. Found Objects d. it had no title originally e. Skyscrapers 1 and 2 10 points Question 35 1. Why do we presume that the head of a woman from Benin (0.18) was made for someone wealthy? a. because it was made to be shown in a museum b. because it strongly resembles the Queen c. because it has a price carved on the back d. because it was made from rare ivory e. it was definitely not made for anyone wealthy 10 points Question 36 1. Shahzia Sikander’s art is best described as Abstract Expressionism Naturalist sculpture Pop Art Miniature Painting 10 points Question 37 1. A sunset is a work of art. True False 10 points Question 38 1. A mens’ urinal became a well known artwork in the 20th century. True False 10 points Question 39 1. Which artist has torn out people’s lawns to design and build edible gardens across the country? Andrea Zittel Fritz Haeg Ruben Ortiz Torres Mark Newport

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Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

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English 1 Professor Nielsen Essay One Topic and Guidelines The Context You are a non-profit organization Director of Fundraising, and your goal is to convince a wealthy individual to make a substantial donation to your cause. Choose from one of the following projects derived from the social issues from the course readings below: 1. The Prison Project: Reducing the incarceration rate and numbers in the U.S. 2. Birth Control Advocacy and Access: Supporting a birth control education and free product distribution in the U.S and/or internationally. 3. LGBT Advocacy: Funding education, campaigning, and lobbying for LGBT rights in the U.S. 4. Equality in Education: Supporting funding and scholarships for schools and individuals from less advantaged populations. 5. Migrant Welfare and Protection: Creating safe housing, food, and education for refugees. 6. Something else related to social justice?????? (See me if you have your own project idea). (animal welfare, women’s advocacy, housing, student loans and tuition affordability, etc.) Make a case for a donation of $2 million dollars to your cause by writing a funding request letter to the potential donor. This request is essentially a persuasive essay designed to convince your reader to support your cause. Below is a suggested format for organizing your letter, as well as guidelines for your work. I. The Basics Due: Tuesday, September 29, at Start of Class (Rough Draft). And Tuesday, October 6, at Start of Class (Final Draft) Length: 3-4 Pgs., double spaced in the correct format (see sample paper format template at the end of this document for format.) Font: Times New Roman, 12PT. Margins: 1 inch all around. See sample format at the end of this document for further formatting information. You are required to submit using this format. Check the sample on page five of this document carefully. Editing: Be sure to use the proofreading guide. In particular, avoid the big five errors. Revising: Read over your draft carefully several times. We will work toward revision together in class, but you will also need to revise on your own. Visit the Learning center if you need extra support. II. Organization and Content (Sample Outline Follows.) Use an organized format for your essay. The best way to ensure strong organization is to map out a plan for the content of your essay, using an outline, clustering, or other graphic representation of your key ideas. One potential format follows. Sample Method of Organizing Your Funding Letter: A. The Opening Paragraph 1. Start with some brief striking details to provide the initial background to your letter: facts, figures, brief description of one aspect of the problem- something compelling. 2. End your paragraph with a statement that briefly announces/introduces your organization without yet going into detail about your mission. State that you are requesting a donation and that your letter will describe the need for this donation. (Your Thesis) B. Body of the Letter: The Problem Make a stronger case for the problem your organization seeks to address by describing several aspects of it, using examples and details, as well as quotes from relevant class readings (be sure to cite these correctly). C. Body of the Letter: What Your Organization Will Do Describe some points of actions your group will take and ways that you will spend donor funds to address aspects of the problem you have already described. Choose three to five specific courses of action. Do not make these two extensive. They should be manageable and practical. D. Your Summary and Conclusion: Asking for Money 1. Briefly restate the problem and your organization’s goals using new wording when possible. 2. Connect the funds you need to your organization’s goals 3. Make your request for money. 4. End with a final compelling statement of why the donor should give. III. Strategies and Guidelines 1. Use the writing process steps to help you through your letter. 2. Use the proofreading guide to help you edit and the Learning Center on campus for support. 5. Cite all quotes with the author and page number. Create a works cited page at the end of your essay for the works you discuss. (See the MLA guide and sample student essays in your textbook for examples and step-by-step help with MLA. You may also pick up a guide at the campus writing center and ask them for extra help.) 6. This is NOT a research essay. Most background information should come from common knowledge, your own prior knowledge and experience, and the readings from class/the text. However, you may choose to include up one additional research source if necessary, provided this is a reliable source that you can cite correctly. Please visit OWL at Purdue University for a complete MLA citation guide. You text also has a chapter on MLA citation. 7. Follow the correct essay format for font, spacing, margins, heading, etc. (SEE sample in this document.) IV. Formatting: You are required to format your essay in the way that follows to receive full credit. • Page number in upper right-hand corner (Use “Insert” and “Pg. #”) • Times New Roman 12 Pt. font • Heading in left corner with title, student name, essay 1 (or 2, etc.), Eng 2, and date • Heading is single spaced • Skip two lines to start typing body of text • Body of text is double spaced • Margins remain at 1 inch all around. • DO NOT skip lines between paragraphs • Indent each paragraph five lines • Use MLA format for citation Continue to the next page for format sample. Title of Your Campaign Project (Choose something compelling.) Student Name Essay 1 English 1 Date Dear _______, Start typing your essay here, two lines down from heading. The body of your essay is double spaced, but the heading is only single spaced. Note the page number in the upper right-hand corner. Note the exact content of the heading. There is no title page for short essays, nor is there a title across the top. For short essays of just a few pages, this format is standard. The title goes at the top of the heading. All words in the title are capitalized except pronouns, prepositions, and articles. Do not make your margins greater that one inch. Make sure you use Times New Roman 12 Point font. Do not include graphics or images of any kind in most essays for this class (see me if you think you have an exception). When you reach the end of your paragraph, just hit return and continue typing. Do not skip lines between your paragraphs or over-indent your paragraphs; indent only five lines as marked in the ruler. Do not attempt to write less for your essay by enlarging the font, margins, or spacing. This paragraph demonstrates a good length for an introduction. You next paragraph should start here. This is the way your essay should look. You may use this template to help you format your essay by saving it to your desktop and keeping the settings. You will, of course, have two to three pages when you finish, but this is what the first page would look like roughly. If you include a quote, be sure to cite the author and page number and to include a works cited page at the end of your essay.

English 1 Professor Nielsen Essay One Topic and Guidelines The Context You are a non-profit organization Director of Fundraising, and your goal is to convince a wealthy individual to make a substantial donation to your cause. Choose from one of the following projects derived from the social issues from the course readings below: 1. The Prison Project: Reducing the incarceration rate and numbers in the U.S. 2. Birth Control Advocacy and Access: Supporting a birth control education and free product distribution in the U.S and/or internationally. 3. LGBT Advocacy: Funding education, campaigning, and lobbying for LGBT rights in the U.S. 4. Equality in Education: Supporting funding and scholarships for schools and individuals from less advantaged populations. 5. Migrant Welfare and Protection: Creating safe housing, food, and education for refugees. 6. Something else related to social justice?????? (See me if you have your own project idea). (animal welfare, women’s advocacy, housing, student loans and tuition affordability, etc.) Make a case for a donation of $2 million dollars to your cause by writing a funding request letter to the potential donor. This request is essentially a persuasive essay designed to convince your reader to support your cause. Below is a suggested format for organizing your letter, as well as guidelines for your work. I. The Basics Due: Tuesday, September 29, at Start of Class (Rough Draft). And Tuesday, October 6, at Start of Class (Final Draft) Length: 3-4 Pgs., double spaced in the correct format (see sample paper format template at the end of this document for format.) Font: Times New Roman, 12PT. Margins: 1 inch all around. See sample format at the end of this document for further formatting information. You are required to submit using this format. Check the sample on page five of this document carefully. Editing: Be sure to use the proofreading guide. In particular, avoid the big five errors. Revising: Read over your draft carefully several times. We will work toward revision together in class, but you will also need to revise on your own. Visit the Learning center if you need extra support. II. Organization and Content (Sample Outline Follows.) Use an organized format for your essay. The best way to ensure strong organization is to map out a plan for the content of your essay, using an outline, clustering, or other graphic representation of your key ideas. One potential format follows. Sample Method of Organizing Your Funding Letter: A. The Opening Paragraph 1. Start with some brief striking details to provide the initial background to your letter: facts, figures, brief description of one aspect of the problem- something compelling. 2. End your paragraph with a statement that briefly announces/introduces your organization without yet going into detail about your mission. State that you are requesting a donation and that your letter will describe the need for this donation. (Your Thesis) B. Body of the Letter: The Problem Make a stronger case for the problem your organization seeks to address by describing several aspects of it, using examples and details, as well as quotes from relevant class readings (be sure to cite these correctly). C. Body of the Letter: What Your Organization Will Do Describe some points of actions your group will take and ways that you will spend donor funds to address aspects of the problem you have already described. Choose three to five specific courses of action. Do not make these two extensive. They should be manageable and practical. D. Your Summary and Conclusion: Asking for Money 1. Briefly restate the problem and your organization’s goals using new wording when possible. 2. Connect the funds you need to your organization’s goals 3. Make your request for money. 4. End with a final compelling statement of why the donor should give. III. Strategies and Guidelines 1. Use the writing process steps to help you through your letter. 2. Use the proofreading guide to help you edit and the Learning Center on campus for support. 5. Cite all quotes with the author and page number. Create a works cited page at the end of your essay for the works you discuss. (See the MLA guide and sample student essays in your textbook for examples and step-by-step help with MLA. You may also pick up a guide at the campus writing center and ask them for extra help.) 6. This is NOT a research essay. Most background information should come from common knowledge, your own prior knowledge and experience, and the readings from class/the text. However, you may choose to include up one additional research source if necessary, provided this is a reliable source that you can cite correctly. Please visit OWL at Purdue University for a complete MLA citation guide. You text also has a chapter on MLA citation. 7. Follow the correct essay format for font, spacing, margins, heading, etc. (SEE sample in this document.) IV. Formatting: You are required to format your essay in the way that follows to receive full credit. • Page number in upper right-hand corner (Use “Insert” and “Pg. #”) • Times New Roman 12 Pt. font • Heading in left corner with title, student name, essay 1 (or 2, etc.), Eng 2, and date • Heading is single spaced • Skip two lines to start typing body of text • Body of text is double spaced • Margins remain at 1 inch all around. • DO NOT skip lines between paragraphs • Indent each paragraph five lines • Use MLA format for citation Continue to the next page for format sample. Title of Your Campaign Project (Choose something compelling.) Student Name Essay 1 English 1 Date Dear _______, Start typing your essay here, two lines down from heading. The body of your essay is double spaced, but the heading is only single spaced. Note the page number in the upper right-hand corner. Note the exact content of the heading. There is no title page for short essays, nor is there a title across the top. For short essays of just a few pages, this format is standard. The title goes at the top of the heading. All words in the title are capitalized except pronouns, prepositions, and articles. Do not make your margins greater that one inch. Make sure you use Times New Roman 12 Point font. Do not include graphics or images of any kind in most essays for this class (see me if you think you have an exception). When you reach the end of your paragraph, just hit return and continue typing. Do not skip lines between your paragraphs or over-indent your paragraphs; indent only five lines as marked in the ruler. Do not attempt to write less for your essay by enlarging the font, margins, or spacing. This paragraph demonstrates a good length for an introduction. You next paragraph should start here. This is the way your essay should look. You may use this template to help you format your essay by saving it to your desktop and keeping the settings. You will, of course, have two to three pages when you finish, but this is what the first page would look like roughly. If you include a quote, be sure to cite the author and page number and to include a works cited page at the end of your essay.

1 IN2009: Language Processors Coursework Part 3: The Interpreter Introduction This is the 3rd and final part of the coursework. In the second part of the coursework you created a parser for the Moopl grammar which, given a syntactically correct Moopl program as input, builds an AST representation of the program. In Part 3 you will develop an interpreter which executes Moopl programs by visiting their AST representations. For this part of the coursework we provide functional code (with limitations, see below) for parsing, building a symbol table, type checking and variable allocation. Marks This part of the coursework is worth 12 of the 30 coursework marks for the Language Processors module. This part of the coursework is marked out of 12. Submission deadline This part of the coursework should be handed in before 5pm on Sunday 9th April 2017. In line with school policy, late submissions will be awarded no marks. Return & Feedback Marks and feedback will be available as soon as possible, certainly on or before Wed 3rd May 2017. Plagiarism If you copy the work of others (either that of fellow students or of a third party), with or without their permission, you will score no marks and further disciplinary action will be taken against you. Group working You will be working in the same groups as for the previous parts of the coursework except where group changes have already been approved. Submission: Submit a zip archive (not a rar file) of all your source code (the src folder of your project). We do not want the other parts of your NetBeans project, only the source code. Note 1: Submissions which do not compile will get zero marks. Note 2: You must not change the names or types of any of the existing packages, classes or public methods. 2 Getting started Download either moopl-interp.zip or moopl-interp.tgz from Moodle and extract all files. Key contents to be aware of: • A fully implemented Moopl parser (also implements a parser for the interpreter command language; see below). • A partially implemented Moopl type checker. • Test harnesses for the type checker and interpreter. • A directory of a few example Moopl programs (see Testing below). • Folder interp containing prototype interpreter code. The type-checker is only partially implemented but a more complete implementation will be provided following Session 6. That version is still not fully complete because it doesn’t support inheritance. Part d) below asks you to remove this restriction. The VarAllocator visitor in the interp package uses a simple implementation which only works for methods in which all parameter and local variable names are different. Part e) below asks you to remove this restriction. The three parts below should be attempted in sequence. When you have completed one part you should make a back-up copy of the work and keep it safe, in case you break it in your attempt at the next part. Be sure to test old functionality as well as new (regression testing). We will not assess multiple versions so, if your attempt at part d) or e) breaks previously working code, you may gain a better mark by submitting the earlier version for assessment. c) [8 marks] The Basic Interpreter: complete the implementation of the Interpreter visitor in the interp package. d) [2 marks] Inheritance: extend the type-checker, variable allocator and interpreter to support inheritance. e) [2 marks] Variable Allocation: extend the variable allocator to fully support blockstructure and lexical scoping, removing the requirement that all parameter and local variable names are different. Aim to minimise the number of local variable slots allocated in a stack frame. Note: variable and parameter names declared at the same scope level are still required to be different from each other (a method cannot have two different parameters called x, for example) and this is enforced by the existing typechecking code. But variables declared in different blocks (even when nested) can have the same name. Exceptions Your interpreter will only ever be run on Moopl code which is type-correct (and free from uninitialised local variables). But it is still possible that the Moopl code contains logical errors which may cause runtime errors (such as null-reference or array-bound errors). Your interpreter should throw a MooplRunTimeException with an appropriate error message in these cases. The only kind of exception your interpreter should ever throw is a MooplRunTimeException. 3 Testing The examples folder does not contain a comprehensive test-suite. You need to invent and run your own tests. The document Moopl compared with Java gives a concise summary of how Moopl programs are supposed to behave. You can (and should) also compare the behaviour of your interpreter with that of the online tool: https://smcse.city.ac.uk/student/sj353/langproc/Moopl.html (Note: the online tool checks for uninitialised local variables. Your implementation is not expected to do this.) To test your work, run the top-level Interpret harness, providing the name of a Moopl source file as a command-line argument. When run on a type-correct Moopl source file, Interpret will pretty-print the Moopl program then display a command prompt (>) at which you can enter one of the following commands: :quit This will quit the interpreter. :call main() This will call the top-level proc main, interpreted in the context defined by the Moopl program. (Any top-level proc can be called this way). :eval Exp ; This will evaluate expression Exp, interpreted in the context defined by the Moopl program, and print the result. Note the required terminating semi-colon. Testing your Expression visitors To unit-test your Exp visit methods, run the top-level Interpret harness on a complete Moopl program (though it can be trivial) and use the :eval command. For example, to test your visit methods for the Boolean-literals (ExpTrue and ExpFalse), you would enter the commands > :eval true ; > :eval false ; which should output 1 and 0, respectively. For the most basic cases, the Moopl program is essentially irrelevant (a single top-level proc with empty body may be sufficient). For other cases you will need to write programs containing class definitions (in order, for example, to test object creation and method call). Testing your Statement visitors To unit-test your Stm visit methods, write very simple Moopl programs, each with a top-level proc main() containing just a few lines of code. Run the top-level Interpret harness on these simple programs and enter the command > :call main() You will find a few examples to get you started in the folder examples/unittests. As for the Exp tests, simple cases can be tested using Moopl programs with just a main proc but for the more complex tests you will need to write Moopl programs containing class definitions. 4 Grading criteria Solutions will be graded according to their functional correctness, and the elegance of their implementation. Below are criteria that guide the award of marks. 70 – 100 [1st class] Work that meets all the requirements in full, constructed and presented to a professional standard. Showing evidence of independent reading, thinking and analysis. 60 – 69 [2:1] Work that makes a good attempt to address the requirements, realising all to some extent and most well. Well-structured and well presented. 50 – 59 [2:2] Work that attempts to address requirements realising all to some extent and some well but perhaps also including irrelevant or underdeveloped material. Structure and presentation may not always be clear. 40 – 49 [3rd class] Work that attempts to address the requirements but only realises them to some extent and may not include important elements or be completely accurate. Structure and presentation may lack clarity. 0 – 39 [fail] Unsatisfactory work that does not adequately address the requirements. Structure and presentation may be confused or incoherent.

1 IN2009: Language Processors Coursework Part 3: The Interpreter Introduction This is the 3rd and final part of the coursework. In the second part of the coursework you created a parser for the Moopl grammar which, given a syntactically correct Moopl program as input, builds an AST representation of the program. In Part 3 you will develop an interpreter which executes Moopl programs by visiting their AST representations. For this part of the coursework we provide functional code (with limitations, see below) for parsing, building a symbol table, type checking and variable allocation. Marks This part of the coursework is worth 12 of the 30 coursework marks for the Language Processors module. This part of the coursework is marked out of 12. Submission deadline This part of the coursework should be handed in before 5pm on Sunday 9th April 2017. In line with school policy, late submissions will be awarded no marks. Return & Feedback Marks and feedback will be available as soon as possible, certainly on or before Wed 3rd May 2017. Plagiarism If you copy the work of others (either that of fellow students or of a third party), with or without their permission, you will score no marks and further disciplinary action will be taken against you. Group working You will be working in the same groups as for the previous parts of the coursework except where group changes have already been approved. Submission: Submit a zip archive (not a rar file) of all your source code (the src folder of your project). We do not want the other parts of your NetBeans project, only the source code. Note 1: Submissions which do not compile will get zero marks. Note 2: You must not change the names or types of any of the existing packages, classes or public methods. 2 Getting started Download either moopl-interp.zip or moopl-interp.tgz from Moodle and extract all files. Key contents to be aware of: • A fully implemented Moopl parser (also implements a parser for the interpreter command language; see below). • A partially implemented Moopl type checker. • Test harnesses for the type checker and interpreter. • A directory of a few example Moopl programs (see Testing below). • Folder interp containing prototype interpreter code. The type-checker is only partially implemented but a more complete implementation will be provided following Session 6. That version is still not fully complete because it doesn’t support inheritance. Part d) below asks you to remove this restriction. The VarAllocator visitor in the interp package uses a simple implementation which only works for methods in which all parameter and local variable names are different. Part e) below asks you to remove this restriction. The three parts below should be attempted in sequence. When you have completed one part you should make a back-up copy of the work and keep it safe, in case you break it in your attempt at the next part. Be sure to test old functionality as well as new (regression testing). We will not assess multiple versions so, if your attempt at part d) or e) breaks previously working code, you may gain a better mark by submitting the earlier version for assessment. c) [8 marks] The Basic Interpreter: complete the implementation of the Interpreter visitor in the interp package. d) [2 marks] Inheritance: extend the type-checker, variable allocator and interpreter to support inheritance. e) [2 marks] Variable Allocation: extend the variable allocator to fully support blockstructure and lexical scoping, removing the requirement that all parameter and local variable names are different. Aim to minimise the number of local variable slots allocated in a stack frame. Note: variable and parameter names declared at the same scope level are still required to be different from each other (a method cannot have two different parameters called x, for example) and this is enforced by the existing typechecking code. But variables declared in different blocks (even when nested) can have the same name. Exceptions Your interpreter will only ever be run on Moopl code which is type-correct (and free from uninitialised local variables). But it is still possible that the Moopl code contains logical errors which may cause runtime errors (such as null-reference or array-bound errors). Your interpreter should throw a MooplRunTimeException with an appropriate error message in these cases. The only kind of exception your interpreter should ever throw is a MooplRunTimeException. 3 Testing The examples folder does not contain a comprehensive test-suite. You need to invent and run your own tests. The document Moopl compared with Java gives a concise summary of how Moopl programs are supposed to behave. You can (and should) also compare the behaviour of your interpreter with that of the online tool: https://smcse.city.ac.uk/student/sj353/langproc/Moopl.html (Note: the online tool checks for uninitialised local variables. Your implementation is not expected to do this.) To test your work, run the top-level Interpret harness, providing the name of a Moopl source file as a command-line argument. When run on a type-correct Moopl source file, Interpret will pretty-print the Moopl program then display a command prompt (>) at which you can enter one of the following commands: :quit This will quit the interpreter. :call main() This will call the top-level proc main, interpreted in the context defined by the Moopl program. (Any top-level proc can be called this way). :eval Exp ; This will evaluate expression Exp, interpreted in the context defined by the Moopl program, and print the result. Note the required terminating semi-colon. Testing your Expression visitors To unit-test your Exp visit methods, run the top-level Interpret harness on a complete Moopl program (though it can be trivial) and use the :eval command. For example, to test your visit methods for the Boolean-literals (ExpTrue and ExpFalse), you would enter the commands > :eval true ; > :eval false ; which should output 1 and 0, respectively. For the most basic cases, the Moopl program is essentially irrelevant (a single top-level proc with empty body may be sufficient). For other cases you will need to write programs containing class definitions (in order, for example, to test object creation and method call). Testing your Statement visitors To unit-test your Stm visit methods, write very simple Moopl programs, each with a top-level proc main() containing just a few lines of code. Run the top-level Interpret harness on these simple programs and enter the command > :call main() You will find a few examples to get you started in the folder examples/unittests. As for the Exp tests, simple cases can be tested using Moopl programs with just a main proc but for the more complex tests you will need to write Moopl programs containing class definitions. 4 Grading criteria Solutions will be graded according to their functional correctness, and the elegance of their implementation. Below are criteria that guide the award of marks. 70 – 100 [1st class] Work that meets all the requirements in full, constructed and presented to a professional standard. Showing evidence of independent reading, thinking and analysis. 60 – 69 [2:1] Work that makes a good attempt to address the requirements, realising all to some extent and most well. Well-structured and well presented. 50 – 59 [2:2] Work that attempts to address requirements realising all to some extent and some well but perhaps also including irrelevant or underdeveloped material. Structure and presentation may not always be clear. 40 – 49 [3rd class] Work that attempts to address the requirements but only realises them to some extent and may not include important elements or be completely accurate. Structure and presentation may lack clarity. 0 – 39 [fail] Unsatisfactory work that does not adequately address the requirements. Structure and presentation may be confused or incoherent.

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Chapter 5 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 5.1 Drawing Force Vectors Learning Goal: To practice Tactics Box 5.1 Drawing Force Vectors. To visualize how forces are exerted on objects, we can use simple diagrams such as vectors. This Tactics Box illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points. TACTICS BOX 5.1 Drawing force vectors Represent the object 1. as a particle. 2. Place the tail of the force vector on the particle. 3. Draw the force vector as an arrow pointing in the proper direction and with a length proportional to the size of the force. 4. Give the vector an appropriate label. The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as a black dot. Part A A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book. Follow the steps above to draw the force vector . Use the black dot as the particle representing the book. F  F push F push Draw the vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Tactics Box 5.2 Identifying Forces Learning Goal: To practice Tactics Box 5.2 Identifying Forces. The first basic step in solving force and motion problems generally involves identifying all of the forces acting on an object. This tactics box provides a step-by-step method for identifying each force in a problem. TACTICS BOX 5.2 Identifying forces Identify the object of interest. This is the object whose motion 1. you wish to study. 2. Draw a picture of the situation. Show the object of interest and all other objects—such as ropes, springs, or surfaces—that touch it. 3. Draw a closed curve around the object. Only the object of interest is inside the curve; everything else is outside. 4. Locate every point on the boundary of this curve where other objects touch the object of interest. These are the points where contact forces are exerted on the object. Name and label each contact force acting on the object. There is at least one force at each point of contact; there may be more than one. When necessary, use subscripts to distinguish forces of the same type. 5. 6. Name and label each long-range force acting on the object. For now, the only long-range force is the gravitational force. Apply these steps to the following problem: A crate is pulled up a rough inclined wood board by a tow rope. Identify the forces on the crate. Part A Which of the following objects are of interest? Check all that apply. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Conceptual Questions on Newton’s 1st and 2nd Laws Learning Goal: To understand the meaning and the basic applications of Newton’s 1st and 2nd laws. In this problem, you are given a diagram representing the motion of an object–a motion diagram. The dots represent the object’s position at moments separated by equal intervals of time. The dots are connected by arrows representing the object’s average velocity during the corresponding time interval. Your goal is to use this motion diagram to determine the direction of the net force acting on the object. You will then determine which force diagrams and which situations may correspond to such a motion. crate earth rope wood board Part A What is the direction of the net force acting on the object at position A? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D upward downward to the left to the right The net force is zero. This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). Part I This question will be shown after you complete previous question(s). Part J This question will be shown after you complete previous question(s). Understanding Newton’s Laws Part A An object cannot remain at rest unless which of the following holds? You did not open hints for this part. ANSWER: Part B If a block is moving to the left at a constant velocity, what can one conclude? You did not open hints for this part. ANSWER: The net force acting on it is zero. The net force acting on it is constant and nonzero. There are no forces at all acting on it. There is only one force acting on it. Part C A block of mass is acted upon by two forces: (directed to the left) and (directed to the right). What can you say about the block’s motion? You did not open hints for this part. ANSWER: Part D A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________. You did not open hints for this part. ANSWER: There is exactly one force applied to the block. The net force applied to the block is directed to the left. The net force applied to the block is zero. There must be no forces at all applied to the block. 2 kg 3 N 4 N It must be moving to the left. It must be moving to the right. It must be at rest. It could be moving to the left, moving to the right, or be instantaneously at rest. Part E Two forces, of magnitude and , are applied to an object. The relative direction of the forces is unknown. The net force acting on the object __________. Check all that apply. You did not open hints for this part. ANSWER: Tactics Box 5.3 Drawing a Free-Body Diagram Learning Goal: To practice Tactics Box 5.3 Drawing a Free-Body Diagram. A free-body diagram is a diagram that represents the object as a particle and shows all of the forces acting on the object. Learning how to draw such a diagram is a very important skill in solving physics problems. This tactics box explains the essential steps to construct a correct free-body diagram. TACTICS BOX 5.3 Drawing a free-body diagram Identify all forces acting on the object. This step was described 1. in Tactics Box 5.2. continuously changing direction moving at constant velocity moving with a constant nonzero acceleration moving with continuously increasing acceleration 4 N 10 N cannot have a magnitude equal to cannot have a magnitude equal to cannot have the same direction as the force with magnitude must have a magnitude greater than 5 N 10 N 10 N 10 N Draw a coordinate system. Use the axes defined in your pictorial representation. If those axes are tilted, for motion along an incline, then the axes of the free-body diagram should be similarly tilted. 2. Represent the object as a dot at the origin of the coordinate axes. This is 3. the particle model. 4. Draw vectors representing each of the identified forces. This was described in Tactics Box 5.1. Be sure to label each force vector. Draw and label the net force vector . Draw this vector beside the diagram, not on the particle. Or, if appropriate, write . Then, check that points in the same direction as the acceleration vector on your motion diagram. 5. Apply these steps to the following problem: Your physics book is sliding on the carpet. Draw a free-body diagram. Part A Which forces are acting on the book? Check all that apply. You did not open hints for this part. ANSWER: F  net F =  net 0 F  net a Part B Draw the most appropriate set of coordinate axes for this problem. The orientation of your vectors will be graded. ANSWER: gravity normal force drag static friction tension kinetic friction spring force Part C This question will be shown after you complete previous question(s). Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points.

Chapter 5 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 5.1 Drawing Force Vectors Learning Goal: To practice Tactics Box 5.1 Drawing Force Vectors. To visualize how forces are exerted on objects, we can use simple diagrams such as vectors. This Tactics Box illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points. TACTICS BOX 5.1 Drawing force vectors Represent the object 1. as a particle. 2. Place the tail of the force vector on the particle. 3. Draw the force vector as an arrow pointing in the proper direction and with a length proportional to the size of the force. 4. Give the vector an appropriate label. The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as a black dot. Part A A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book. Follow the steps above to draw the force vector . Use the black dot as the particle representing the book. F  F push F push Draw the vector starting at the black dot. The location and orientation of the vector will be graded. The length of the vector will not be graded. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Tactics Box 5.2 Identifying Forces Learning Goal: To practice Tactics Box 5.2 Identifying Forces. The first basic step in solving force and motion problems generally involves identifying all of the forces acting on an object. This tactics box provides a step-by-step method for identifying each force in a problem. TACTICS BOX 5.2 Identifying forces Identify the object of interest. This is the object whose motion 1. you wish to study. 2. Draw a picture of the situation. Show the object of interest and all other objects—such as ropes, springs, or surfaces—that touch it. 3. Draw a closed curve around the object. Only the object of interest is inside the curve; everything else is outside. 4. Locate every point on the boundary of this curve where other objects touch the object of interest. These are the points where contact forces are exerted on the object. Name and label each contact force acting on the object. There is at least one force at each point of contact; there may be more than one. When necessary, use subscripts to distinguish forces of the same type. 5. 6. Name and label each long-range force acting on the object. For now, the only long-range force is the gravitational force. Apply these steps to the following problem: A crate is pulled up a rough inclined wood board by a tow rope. Identify the forces on the crate. Part A Which of the following objects are of interest? Check all that apply. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Conceptual Questions on Newton’s 1st and 2nd Laws Learning Goal: To understand the meaning and the basic applications of Newton’s 1st and 2nd laws. In this problem, you are given a diagram representing the motion of an object–a motion diagram. The dots represent the object’s position at moments separated by equal intervals of time. The dots are connected by arrows representing the object’s average velocity during the corresponding time interval. Your goal is to use this motion diagram to determine the direction of the net force acting on the object. You will then determine which force diagrams and which situations may correspond to such a motion. crate earth rope wood board Part A What is the direction of the net force acting on the object at position A? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Part D upward downward to the left to the right The net force is zero. This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Part H This question will be shown after you complete previous question(s). Part I This question will be shown after you complete previous question(s). Part J This question will be shown after you complete previous question(s). Understanding Newton’s Laws Part A An object cannot remain at rest unless which of the following holds? You did not open hints for this part. ANSWER: Part B If a block is moving to the left at a constant velocity, what can one conclude? You did not open hints for this part. ANSWER: The net force acting on it is zero. The net force acting on it is constant and nonzero. There are no forces at all acting on it. There is only one force acting on it. Part C A block of mass is acted upon by two forces: (directed to the left) and (directed to the right). What can you say about the block’s motion? You did not open hints for this part. ANSWER: Part D A massive block is being pulled along a horizontal frictionless surface by a constant horizontal force. The block must be __________. You did not open hints for this part. ANSWER: There is exactly one force applied to the block. The net force applied to the block is directed to the left. The net force applied to the block is zero. There must be no forces at all applied to the block. 2 kg 3 N 4 N It must be moving to the left. It must be moving to the right. It must be at rest. It could be moving to the left, moving to the right, or be instantaneously at rest. Part E Two forces, of magnitude and , are applied to an object. The relative direction of the forces is unknown. The net force acting on the object __________. Check all that apply. You did not open hints for this part. ANSWER: Tactics Box 5.3 Drawing a Free-Body Diagram Learning Goal: To practice Tactics Box 5.3 Drawing a Free-Body Diagram. A free-body diagram is a diagram that represents the object as a particle and shows all of the forces acting on the object. Learning how to draw such a diagram is a very important skill in solving physics problems. This tactics box explains the essential steps to construct a correct free-body diagram. TACTICS BOX 5.3 Drawing a free-body diagram Identify all forces acting on the object. This step was described 1. in Tactics Box 5.2. continuously changing direction moving at constant velocity moving with a constant nonzero acceleration moving with continuously increasing acceleration 4 N 10 N cannot have a magnitude equal to cannot have a magnitude equal to cannot have the same direction as the force with magnitude must have a magnitude greater than 5 N 10 N 10 N 10 N Draw a coordinate system. Use the axes defined in your pictorial representation. If those axes are tilted, for motion along an incline, then the axes of the free-body diagram should be similarly tilted. 2. Represent the object as a dot at the origin of the coordinate axes. This is 3. the particle model. 4. Draw vectors representing each of the identified forces. This was described in Tactics Box 5.1. Be sure to label each force vector. Draw and label the net force vector . Draw this vector beside the diagram, not on the particle. Or, if appropriate, write . Then, check that points in the same direction as the acceleration vector on your motion diagram. 5. Apply these steps to the following problem: Your physics book is sliding on the carpet. Draw a free-body diagram. Part A Which forces are acting on the book? Check all that apply. You did not open hints for this part. ANSWER: F  net F =  net 0 F  net a Part B Draw the most appropriate set of coordinate axes for this problem. The orientation of your vectors will be graded. ANSWER: gravity normal force drag static friction tension kinetic friction spring force Part C This question will be shown after you complete previous question(s). Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points.

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. Pt 1. Making Observations (Introduction) Write a brief, introductory paragraph that includes general observations related to the topic. You may consider information from the news, media (tv, movies), social media, popular views, ideas from the general public, or your personal experiences. Your paragraph should specifically mention three (3) observations related to this topic and be sure to cite your sources. You should also include your thoughts on why this topic is of interest to you or relevant to society (i.e. what is the significance?). Pt 2. Apply The Content Choose five (5) terms or concepts that we have covered in this unit that are related to the chosen topic. Define each term in your own words and then write one (1) sentence that explains how it is related to the topic. The concept are: Define evolution. What was Darwin’s role in establishing the theory of evolution? What does the phrase “descent with modification” mean? How are fossils, anatomical studies, and molecular biology used to provide evidence for the theory of evolution? What is “fitness” in a biological organism? What role do mutations have in natural selection? What are the types of natural selection? How do they effect the genetic variation in a population? What is genetic drift? gene flow? How do they effect the genetic variation in a population? What forces can lead to adaptive evolution? What is the biological definition of a species? What are the three domains of living organisms? What are the six kingdoms? For each kingdom you should be able to describe the cellular structure, means of reproduction, ways of getting nutrients/food, general/adaptive features, and an example organism. How does Helicobacter pylori avoid competition? What extreme environment does a hermoacidophile occupy? What is unique about the Volvox compared to other protists? How do pitcher plants thrive in low nutrient environments? How does the puffball mushroom achieve reproductive success? What adaptations allowed plants to live on the land? What major adaptations occurred in the animal kingdom? In vertebrates? What domain, kingdom, phylum, sub phylum, and class do humans belong to? What do we share with organisms in these groups? What are the ecological levels of the biological hierarchy? What are the elements of a habitat? What are the criteria used by ecologists to measure and observe populations? What common patterns of population distribution are seen in nature? Compare the three kinds of survivorship curves? What do they show? What kind of reproductive behaviors lead to type I, II, and III survivorship curves? How does idealized population growth differ from how actual populations grow? What are factors that affect the growth of a population? How do density-dependent factors affect population growth? What are examples of density-independent factors that can affect population growth? What is a population boom? What is a population bust? Describe the boom and bust cycles often observed in nature. What kinds of competition occur in a habitat? What kinds of symbiotic relationships occur in a habitat? How do organisms avoid predation? What are the levels in a trophic structure? How can plants and animals avoid being eaten? Why is a food web a more accurate representation of the organisms in a community compared to a food chain? Why are most food chains limited to only three or four trophic levels.What are some common threats to biodiversity? What are common types of pollution? Explain why we must be concerned about even small levels of polluting chemicals in the environment. What is sustainability? How can we contribute to the sustainability of life on our planet? Pt 3. Form A Claim Write a claim statement related to the chosen topic. Consider the major question that you are addressing and then develop a statement that will guide your research and writing as you develop your scientific explanation (in Pt 4). Pt 4. Construct a Scientific Explanation Write a scientific explanation that includes evidence and reasoning to support your claim. Your explanation should demonstrate your understanding of the chosen topic using discussion and content from this course as a starting point. Your explanation should include information from a minimum of three (3) sources and one (1) of these sources must be a peer-reviewed scientific article or a review of a scientific study or studies (i.e. a primary or secondary source). You should cite your sources within the body of your explanation and include a list of references at the end (any standard formatting method is acceptable).

. Pt 1. Making Observations (Introduction) Write a brief, introductory paragraph that includes general observations related to the topic. You may consider information from the news, media (tv, movies), social media, popular views, ideas from the general public, or your personal experiences. Your paragraph should specifically mention three (3) observations related to this topic and be sure to cite your sources. You should also include your thoughts on why this topic is of interest to you or relevant to society (i.e. what is the significance?). Pt 2. Apply The Content Choose five (5) terms or concepts that we have covered in this unit that are related to the chosen topic. Define each term in your own words and then write one (1) sentence that explains how it is related to the topic. The concept are: Define evolution. What was Darwin’s role in establishing the theory of evolution? What does the phrase “descent with modification” mean? How are fossils, anatomical studies, and molecular biology used to provide evidence for the theory of evolution? What is “fitness” in a biological organism? What role do mutations have in natural selection? What are the types of natural selection? How do they effect the genetic variation in a population? What is genetic drift? gene flow? How do they effect the genetic variation in a population? What forces can lead to adaptive evolution? What is the biological definition of a species? What are the three domains of living organisms? What are the six kingdoms? For each kingdom you should be able to describe the cellular structure, means of reproduction, ways of getting nutrients/food, general/adaptive features, and an example organism. How does Helicobacter pylori avoid competition? What extreme environment does a hermoacidophile occupy? What is unique about the Volvox compared to other protists? How do pitcher plants thrive in low nutrient environments? How does the puffball mushroom achieve reproductive success? What adaptations allowed plants to live on the land? What major adaptations occurred in the animal kingdom? In vertebrates? What domain, kingdom, phylum, sub phylum, and class do humans belong to? What do we share with organisms in these groups? What are the ecological levels of the biological hierarchy? What are the elements of a habitat? What are the criteria used by ecologists to measure and observe populations? What common patterns of population distribution are seen in nature? Compare the three kinds of survivorship curves? What do they show? What kind of reproductive behaviors lead to type I, II, and III survivorship curves? How does idealized population growth differ from how actual populations grow? What are factors that affect the growth of a population? How do density-dependent factors affect population growth? What are examples of density-independent factors that can affect population growth? What is a population boom? What is a population bust? Describe the boom and bust cycles often observed in nature. What kinds of competition occur in a habitat? What kinds of symbiotic relationships occur in a habitat? How do organisms avoid predation? What are the levels in a trophic structure? How can plants and animals avoid being eaten? Why is a food web a more accurate representation of the organisms in a community compared to a food chain? Why are most food chains limited to only three or four trophic levels.What are some common threats to biodiversity? What are common types of pollution? Explain why we must be concerned about even small levels of polluting chemicals in the environment. What is sustainability? How can we contribute to the sustainability of life on our planet? Pt 3. Form A Claim Write a claim statement related to the chosen topic. Consider the major question that you are addressing and then develop a statement that will guide your research and writing as you develop your scientific explanation (in Pt 4). Pt 4. Construct a Scientific Explanation Write a scientific explanation that includes evidence and reasoning to support your claim. Your explanation should demonstrate your understanding of the chosen topic using discussion and content from this course as a starting point. Your explanation should include information from a minimum of three (3) sources and one (1) of these sources must be a peer-reviewed scientific article or a review of a scientific study or studies (i.e. a primary or secondary source). You should cite your sources within the body of your explanation and include a list of references at the end (any standard formatting method is acceptable).

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