7/27/2019 UCLA Math 61 Syllabus and Schedule

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Math 61, Introduction to Discrete StructuresLecture 1, Summer Session A, 2013

Instructor: Will ConleyOffice: MS 6322Office Hours: (tentatively) Tuesdays 3:304:30pm, Thursdays 1:002:00pm, also by appointmentEmail: wconley@ucla.eduWebsite: http://www.math.ucla.edu/~wconley/

Lectures: MTW 1:002:50pm, Geology 3656Each lecture will be broken up into two 50-minute lectures, with a 10-minute break in between.Discussion Sections: T and Th 10:0010:50am or 11:0011:50amTA: Scott GarrabrantCourse Website: https://ccle.ucla.edu/course/view/131A-MATH61-1

Prerequisite: Math 31A and 31B (recommended: the whole 3133 series)

Text:Discrete Mathematics, Seventh Edition, by Richard Johnsonbaugh.We will cover much of the core material in chapters 1, 2, and 3, plus selected topics from chapters 6, 7,8, 9, and/or 10, and possibly topics from chapters 11 and 12 depending on time and the wishes of theclass.

Grading: Your final average in this class will be computed using the following weights:Homework: 15%

Midterm: 35%Final exam: 50%

Homework and Quizzes: Homework will be assigned in lecture each week on Monday, and posted onthe course website. It will generally be collected the following Monday in lecture, except in the lastweek of class. It will be graded and returned to you as soon as possible. Your score on each homeworkassignment will be based on a few randomly chosen problems, as well as overall completion of theassignment. Late homework will not be accepted, but your lowest homework score will be dropped.

Exams: During the exams, you may not use notes, calculators, cell phones, or anything other thanpaper and pencil. There will be no make-ups for missed midterms. If you absolutely must miss themidterm for a legitimate, documented reason, the final exam will be reweighted to 85%, to cover boththe midterm and final. You must take the final exam in order to pass the class. Make-ups for the finalexam are permitted only under exceptional circumstances as outlined in the UCLA student handbook

7/27/2019 UCLA Math 61 Syllabus and Schedule

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Course Outline (Tentative)

Week Date # Sections Topics

Mon, Jun 24

1

1 1.1 Basic set theory

2 1.1 More basic set theory

Tue, Jun 253 1.2 Logic: Propositions, conjunction, disjunction, conditionals

4 1.2, 1.3 Logic: Truth tables, quanti ers

Wed, Jun 265 2.1 Proof techniques: Direct proof, counterexamples

Review

Mon, Jul 1

2

6 2.2 Proof techniques: Proofs by contrapositive, contradiction, cases, proving logical equivalences, etc

7 2.4 Proof techniques: Mathematical induction

Tue, Jul 2

8 3.3 Relations on sets

9 3.4 Equivalence relations and quotients

Wed, Jul 310 3.1 Functions

Review

Mon, Jul 8

3

11 N/A Injectivity, surjectivity, bijectivity

12 N/A Cardinality of sets ("levels" of in nity, countable vs. uncountable, etc)

Tue, Jul 913 6.1 Basic counting principles

14 6.2 Permutations and combinations

Wed, Jul 10

Exam Midterm (Covers the material before chapter 6)

15 6.3 Generalized permutations and combinations

Mon, Jul 15

4

16 6.7 Binomial coe cients

17 6.8 Pigeonhole principle

Tue, Jul 1618 8.1 Examp es o grap s

19 8.2, 8.3 Paths and cycles

Wed, Jul 1720 8.4 Shortest-path algorithm

Review

Mon, Jul 22

5

21 8.5 Representation of graphs

22 8.6 Isomorphisms of graphs

Tue, Jul 2323 8.7 Planar graphs

24 9.1 Examples of trees

Wed, Jul 2425 9.2 More trees

Review

Mon, Jul 29

6

26 9.3, 9.4 Minimal spanning trees

27 9.5 Binary trees

Tue, Jul 3028 7.3, 9.7 Decision trees, sorting (including merge sort from 7.3)

29 9.8 Isomorphic trees

Final exam (1:00-3:00pm)ExamWed, Jul 31