Course Description: Logic, mathematical induction, sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.
Instructor: Nikhil Srivastava, email: firstname at math.obvious.edu
Lectures: TTh 3:305:00pm, F295 Haas Auditorium.
Office Hours: Tuesday 5:156:15pm and Wednesday 2:304:30pm, 1035 Evans Hall.
Course Control Number: 54008.
Announcements
You are not allowed to bring any books, notes, calculators, or scratch paper to any exam.
Homework problems from the textbook will be assigned on the schedule below. All problems assigned in a week will be due in your discussion section the Wednesday of the following week. Late homework will not be accepted. Questions marked with an x are optional.
You are allowed and encouraged to collaborate on the homework, as long as you write up your own solutions and indicate who you worked with. The latter part is absolutely crucial since mathematical writing is one of the main skills you will learn in this course. All problems which say ``show that...'' are asking for a rigorous mathematical proof, and all proofs should be written in complete English sentences.
Complete solutions for each assignment will be posted on this webpage on the due date. One or two problems each week will be graded by the GSIs. When calculating grades, your two lowest homework scores will be dropped.
Do not wait until the last day to do homework. One difference between this course and previous math courses you may have taken is that you will typically not know how to do a problem when you first see it. The process of interpreting a new mathematical statement and constructing a proof establishing its truth or falsehood can be far from straightforward, and is usually less mechanical than the computational problems which you may be more used to. You will often try many things before you find one that works, and you will spend some time being stuck. This is to be expected, and is typical of any creative activity.
Date  Topics  Readings  Homework problems  Remarks 
T 1/19  Intro, propositional logic  § 1.11.3 
§ 1.1: 7, 9bdf, 12bdf, 18, 23, 27 § 1.2: 5, 16, 18 § 1.3: 7, 9, 11, 21  
Th 1/21  Predicates, quantifiers, rules of inference  § 1.41.6 
§ 1.4: 7, 9, 15, 19, 43 § 1.5: 9ace, 20, 25, 30 § 1.6: 2, 3bd, 6, 7, 15, 19  
T 1/26  Finish rules of inference, Proofs  § 1.6, 1.7, 1.8 
§ 1.7: 1, 8, 12, 16, 18, 24 § 1.8: 10, 14, 18, 24, 34  
Th 1/28  Sets and functions  § 2.12.3 
§ 2.1: 10, 18, 22, 26, 42, 46. § 2.2: 12, 16de, 18cd, 26bc, 48. § 2.3: 1, 4bc, 14, 20.  
T 2/2  Finish functions, sequences, cardinality  § 2.3, 2.4, 2.5 
§ 2.3: 28, 34, 40, 44. § 2.4: 26ace, 32, 34, 46. § 2.5: 2, 10, 20, 40x.  skip recurrences for now x means optional 
Th 2/4  Modular arithmetic, integer representations  § 4.1, 4.2 
§ 4.1: 16, 24, 30, 37, 38, 39. § 4.2: 2, 4, 28, 32.  
T 2/9  Primes, GCD, Euclidean algorithm .  § 4.3  § 4.3: 4aef, 6x, 11, 16ad, 28, 32abc, 36x, 40, 49, 52.  
Th 2/11  Inverses, Chinese Remainder Theorem, Fermat's Little Theorem  § 4.4  § 4.4: 2, 6bc, 7, 12bc, 16, 17, 20, 29, 30, 38.  
T 2/16  Cryptography, RSA, and review  § 4.6  § 4.6: 24, 28.  
Th 2/18  MIDTERM 1 (in class)  
T 2/23  Mathematical Induction  § 5.1, 5.2 
§ 5.1: 4, 10, 19, 36, 49, 54x, 55x, 62x, 64, 72x. § 5.2: 4, 9, 12, 14, 36. 
x means optional and difficult, but recommended 
Th 2/25  Recursive definitions  § 5.3  § 5.3: 4, 6, 8, 12, 14, 17, 20  
T 3/1  Counting and the Pigeonhole Principle  § 6.1, 6.2 
§ 6.1: 8, 16, 22af, 26, 40. § 6.2: 4, 10, 23, 26, 27, 31, 38x. 

Th 3/3  Permutations, combinations, binomial coefficients  § 6.3, 6.4 
§ 6.3: 12, 16, 18, 21, 24 § 6.4: 8, 10, 14, 16, 20, 22. 

T 3/8  generalized permutations and combinations  § 6.5  § 6.5: 10, 11, 16, 18, 20, 24, 26x, 47.  indistinguishable boxes is skipped for now 
Th 3/10  Intro to probability  § 7.1  § 7.1: 6, 18, 19, 20, 34, 36, 38.  
T 3/15  Probability theory, conditional probability, independence  § 7.2  § 7.2: 12, 13, 15, 16, 17, 18, 24, 25, 26, 27ac.  skip probabilistic method, algorithms 
Th 3/17  Bayes' rule  § 7.27.3  § 7.2: 34 § 7.3: 6, 10, 12, 16. § 7.4: 4,7. 

SPRING BREAK  
T 3/29  Random variables, expectation  § 7.4  § 7.4: 10, 12, 16, 24, 25, 32, 36, 37, 38, 48.  
Th 3/31  Variance, review  Chapters 1 and 2, 5.15.3, 6.16.5, 7.17.4.  practice Midterm 2  
T 4/5  MIDTERM 2 (in class)  
Th 4/7  Recurrence relations, generating functions  8.1, 8.4  § 8.1: 1, 3, 6x, 8, 12, 29x, 32x § 8.2: 17 § 8.4: 6cd, 8ad, 10b, 32, 34. 

T 4/12  Generating Functions, InclusionExclusion  8.48.6  § 8.4: 18, 19, 30ace, 39, 41x, 43. § 8.5: 14, 22x, 24, 26. § 8.6: 2, 8, 14, 16, 18x. 
Note: the book starts Fibonacci at 1, not 0. 
Th 4/14  Relations, equivalence relations  9.1, 9.5 
§ 9.1: 6adh, 10, 47x, 49. § 9.3: 2b, 4b, 19b, 24, 32. § 9.5: 2bcd, 3abc, 10, 16, 18, 22, 46, 49, 68x. 

T 4/19  Intro to graphs, examples, bipartite graphs  10.1, 10.2  § 10.1: 11, 13. § 10.2: 5, 18, 20abcd (read examples in 10.2), 26, 35abd, 42abc, 44x, 52, 64. 
Supplementary notes from CS70. 
Th 4/21  More on bipartiteness, connectivity, coloring  10.4  § 10.4: 28, 29, 30, 32, 34, 36, 37x, 38, 43, 45x, 64x.  skip 10.3 for now 
T 4/26 
More coloring, Euler  10.5  § 10.5: 2, 4, 10 § 10.8: 17, 18 + problems not in the book 
HW not graded, but will be on the exam. 
Th 4/28  Finish Euler circuits, matchings, social networks.  no homework  
Tu 5/3 (RRR)  Review session in class (Nikhil)  
Th 5/5 (RRR)  Review session in class (Nick and Julian)  
Fri 5/13  FINAL EXAM (7:00pm10:00pm) 