# Mathematics 55

#### Spring, 2019 TuTh 12:30-2PM, 2050 VLSB

Logic, mathematical induction, sets, relations, and functions. Introduction to graphs, elementary number theory, combinatorics, algebraic structures, and discrete probability theory.
 Professor Kenneth A. Ribet email: Telephone: 510 642 0648 Fax: (510) 642-8204 Office hours (885 Evans Hall)
"If you want to get to know him, you can, and even if you don't, you will."

#### Textbook

The catalog description corresponds to the following sections of the textbook:

• Chapter 1: all sections
• Chapter 2: sections 1-5
• Chapter 4: sections 1-4 and section 6
• Chapter 5: sections 1-3
• Chapter 6: sections 1-5
• Chapter 7: all sections
• Chapter 8: sections 1-2 and sections 4-6
• Chpater 9: sections 1, 3, 4 and 5
• Chapter 10: sections 1-5
• Chapter 11: section 1 and Cayley's formula
Because there is a tremendous amount of material in the course, it is imperative to read ahead in the book before each lecture. I welcome comments and questions during the lectures and would especially like to hear from you before each lecture as to what aspects of the material you would like me to emphasize.

#### Examinations

• First midterm exam, Thursday, February 21, 2019, in class
• Last midterm exam, Thursday, April 4, 2019, in class
• Final examination, Thursday, May 16, 2019, 3PM
Please do not plan travel on the dates of these exams. If you believe that you have a conflicting obligation because of an intercollegiate sport or other extracurricular activity, please read these guidelines immediately.

#### Class schedule

DateThemes SectionsHomework problems
Jan. 22
 Intro to the course Propositions and such
§§ 1.1-1.3
 §1.1: §1.2: §1.3:
Jan. 24Quantifiers, rules of inference§§ 1.4-1.6
 §1.4: §1.5: §1.6:
Jan. 29Proofs §§ 1.6-1.8
 §1.7: §1.8:
Jan. 31 Sets, functions and more §§ 2.1-2.3
 §2.1: §2.2: §2.3:
Feb. 5 Sequences, cardinality §§ 2.4-2.5
 §2.4: §2.5:
Feb. 7 The beginning of number theory! §§ 4.1-4.2
 §4.1: §4.2:
Feb. 12 More number theory § 4.3 §4.3:
Feb. 14 Consequences of Bézout's theorem § 4.4 §4.4:
Feb. 19 Crpyto and some review § 4.6 §4.6:
Feb. 21 First Midterm Exam
Feb. 26 Induction §§ 5.1-5.2
 §5.1: §5.2:
Feb. 28 Recursive definitions § 5.3 §5.3:
Mar. 5 Counting and the pigeonhole principle §§ 6.1-6.2
 §6.1: §6.2:
Mar. 7 Permutations, combinations, binomials §§ 6.3-6.4
 §6.3: §6.4:
Mar. 12 More permutations and combinations § 6.5 §6.5:
Mar. 14 Probability begins! §§ 7.1-7.2
 §7.1: §7.2:
Mar. 19 Bayes §§ 7.2-7.3 §7.3:
Mar. 21 Expected value and variance § 7.4 §7.4:
Apr. 2 Expected values and Review
Apr. 4 Second Midterm Exam
Apr. 9 Recurrence relations §§ 8.1-8.2
 §8.1: §8.2:
Apr. 11 Generating functions, inclusion-exclusion §§ 8.4-8.6
 §8.4: §8.5: §8.6:
Apr. 16 Relations § 9.1, § 9.3
 §9.1: §9.3:
Apr. 18 More on relations §§ 9.4-9.5
 §9.4: §9.5:
Apr. 23 Less on graphs §§ 10.1-10.2
 §10.1: §10.2:
Apr. 25 More on graphs §§ 10.3-10.4
 §10.3: §10.4:
Apr. 30 Planar graphs § 10.7 §10.7:
May 2 Euler and Hamilton paths and circuits § 10.5 §10.5:
May. 7 Review
May. 9 Questions
May. 16 Final Exam, 3:00-6:00PM

#### Homework

Homework will be due in your discussion section on Wednesdays:
1. January 30: sections 1.1-1.5
2. February 6: sections 1.6-1.8 and 2.1-2.3
3. February 13: sections 2.4-2.5 and section 4.1
4. February 20: sections 4.2-4.4
5. February 27: sections 4.6 and 5.1
6. March 6: sections 5.2-5.3
7. March 13: sections 6.1-6.3
8. March 20: sections 6.4-6.5, 7.1-7.2
9. April 3: sections 7.3, 7.4
10. April 10: these problems from §7.4: 21, 24, 28, 32, 35
11. April 17: sections 8.1-8.2
12. April 24: sections 8.4-8.6 and section 9.1
13. May 1: sections 9.3-9.5 and section 10.1
14. May 8 (RRR period): sections 10.2-10.5 and 10.7
Each assignment will be worth 12 points. Your homework grade will be the sum of your twelve highest grades and half of your next-to-lowest grade. Accordingly, the maximum possible homework grade will be 150; we are "dropping" your lowest 1 1/2 grades.

#### Grading

Course grades will be based on a composite numerical score that is intended to weight the course components roughly as follows: midterm exams 17% each, homework and quizzes 20%, final exam 46%.

Incomplete grades will be assigned only to students for whom a documented medical, personal or family emergency precludes completion of the course. Students receiving such grades are required to have been doing work of passing quality up to the intervention of the emergency.

The grade distribution for this course has historically been as follows: 31% A, 34% B, 24% C, 11% D/F.

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