Discrete Mathematics
Peter Koroteev, UC Berkeley
Summer Course Format:
In-class lectures, discussion, and online office hours (total 10 hrs per week). Office hours by zoom and in person.
Time and Place: M-Th 8:00-10:00. The room is 3109 Etcheverry Hall.
Textbook: K. Rosen, "Discrete mathematics and its applications" (8th edition)
Description: Logic, mathematical induction sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.Outline of the Course:
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Week 1: Introduction, Propositional logic, quantifiers, proofs. Homework 1: 1.1 (17,31,41,43); 1.2 (15, 43); 1.3 (29, 41); 1.4 (15); 1.5 (27); 1.6 (23, 27); 1.7 (25); 1.8 (27, 39) Videos from N. Shrivastava: [Logic, Proofs] |
Chapter 1
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Week 2: Sets, Operations with sets, functions, sequences Homework 2: 2.1 (7, 23, 32, 41); 2.2 (2, 14, 26, 42); 2.3 (6, 12, 20, 44); 2.4 (26, 34); 2.5: 2 iPad lecture notes: [Week 2]Videos: [Russell's Paradox] |
Chapter 2
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Week 3 : Introduction to Number Theory. Primes, GCD, Euclidean algorithm, Little Fermat theorem, RSA. Midterm 1 Homework 3: 4.1 (16,24,30,39); 4.2 (2,28); 4.3 (4aef, 11, 16ad, 36x, 49, 52); 4.4: (2, 12bc, 6, 17, 30) iPad lecture notes: [Week 3] |
Chapter 4
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Week 4 : Linear Congruences, Little Fermat Theorem, RSA. Combinatorics iPad lecture notes: [Number Theory] |
Chapter 4
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Week 5 : Counting, The Pigeonhole principle, Permutations and Combinaitons. Binomial coefficients Homework 4: 6.2 (9, 16, 27, 28); 6.3 (5, 18,20, 22); 6.4 (8, 22, 24, 33); 6.5 (10, 15, 22, 47) iPad lecture notes:[Combinatorics] Slides on Partitions:[Partitions] |
Chapter 6
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Week 6 : Discrete Probability, Bayes rules, Random variables, Distributions of probability Midterm 2. Homework 5: 7.1 (6, 8, 16, 24, 31); 7.2 (5, 8, 11, 17, 20); 7.3 (3, 6, 8, 12, 16); 7.4 (6, 10, 12, 16, 25, 36)
iPad lecture notes:[Probability]
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Chapter 7
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Weeks 7,8 : Graph theory, advanced counting methods. Final 8/12 Homework 6: 10.1 (2, 4, 8, 12, 13c); 10.2 (4, 5, 6, 12, 26); 10.3 (4, 8, 10, 16, 32, 75); 10.4 (2, 6, 16, 19, 20); 10.5 (2, 6, 9, 14, 18); 10.7 (1, 4, 12, 14, 16). iPad lecture notes [Graph Theory] |
Chapter 10
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Additional Materials: Math 55 Introduction to Proofs by M. Hutchings Archive of exams and midterms on [Tau Beta Pi]