Intro to Abstract Math
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There is no textbook for this course. All lecture notes will be scanned and posted right here. Office Hours: Mon 1-2pm, Thurs 2-3pm, and by appointment. | ||
| Item | Date | Information |
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Homework 1 Solutions |
Wed Sept 9 |
Course Notes What is a Theorem? The Pythagorean Theorem Euclid's Elements Euclid Handout Euclid's Proof of Prop I.47 Definition of "Euclidean Space" |
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Homework 2 Solutions |
Wed Sept 23 |
Course Notes Square Root of 2, 3, 5 Proof by Contradiction Boolean Functions Truth Tables Contrapositive, De Morgan's Law Definition of "Limit" |
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Exam1
Solutions |
Fri Sept 23 |
Total: 24 points A = 21-23 (7 students) B = 16-20 (7 students) C = 11-15 (7 students) [Note: These ranges are very rough.] |
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Homework 3 Solutions |
Mon Oct 12 |
Course Notes The Definition of Z Axioms of Addition Axioms of Multiplication Axioms of Order The Well-Ordering Axiom Definition of "Induction" |
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Homework 4 Solutions |
Wed Oct 28 |
Course Notes The Division Theorem Greatest Common Divisor The (Extended) Euclidean Algorithm Bézout's Identity Euclid's Lemma Fundamental Theorem of Arithmetic |
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Exam2
Solutions |
Fri Oct 30 |
Total: 24 points A = 20-22 (8 students) B = 16-19 (6 students) C = 11-15 (6 students) [Note: These ranges are very rough.] |
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Homework 5 Solutions |
Wed Nov 18 |
Course Notes Applications of the FTA Euclid's Proof of Infinite Primes Equivalence Relations Modular Arithmetic Fermat's little Theorem |
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Homework 6 Solutions |
Fri Dec 4 |
Course Notes The Binomial Theorem The Freshman's Dream Euler's Proof of FlT RSA Cryptosystem |
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Exam3
Solutions |
Mon Dec 7 | |