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You are here: Homepage » People » Graduate Students » Christopher Eppolito » Discrete Math (Spring 2019)

people:grads:eppolito:math314-02-s19

This is the official website of math314-02-s19.^{1)} Please read our syllabus…

**Our Midterm Exam is scheduled for 15 March 2019.**

Here are documents on basic proof techniques and proof-writing style for your own reference.

**Meetings**: Monday, Wednesday, Friday 8am - 9:30am in WH G02

**Office Hours**: Tuesday 10am - 1pm in WH236 (or by appointment in WH310)

**Textbook**: Mathematics for Computer Science (Lehman, Leighton, Meyer)

**Grading**: See the course syllabus for a grade distribution.

**Content**: Propositional logic, methods of proof, naive set theory, functions and relations, induction and recursion, counting, and basic graph theory.

**W 23 Jan 2019**: (Class 1)

- Discussed Syllabus
- Brief introduction to propositional logic (what is meant by the terms
*statement*,*connective*, etc.) **HW**: Read textbook section 3.1 (4 pages)

**F 25 Jan 2019**: (Class 2)

- Translation of English statements into the formal language
- Truth tables (optional: read textbook section 3.2)
**Practice**: problem set 1**HW**: Read textbook sections 3.3 and 3.4 (2 pages and 5 pages)

**M 28 Jan 2019**: (Class 3)

- Quiz: Truth table construction
- Validity, satisfiability, and logical equivalence
- Developed several basic equivalences of propositional statements.

**W 30 Jan 2019**: (Class 4)

- Disjunctive Normal Form and Conjunctive Normal Form
- Algebra of propositions (textbook section 3.4)
**Practice**: problem set 2**HW**: Read textbook section 3.6 (5 pages)

**F 1 Feb 2019**: (Class 5)

- Quantified predicate logic (textbook section 3.6)

**M 4 Feb 2019**: (Class 6)

- Basics of sets (textbook section 4.1)
- Example proofs involving sets (direct proof)

**W 6 Feb 2019**: (Class 7)

- More proofs of set theoretic identities (proof by cases, proof via a string of equivalent statements).
- Introduced general relations (lots of examples)
- Defined equivalence relations
**HW**: Read about functions and relations for Friday's class (caution: I'm NOT following the textbook here!)

**F 8 Feb 2019**: (Class 8)

- Equivalence relations (many examples)
- Introduction to functions (defined injective, surjective, and bijective)
**Written Homework 1**: Complete this list of problems (Due 15 Feb 2019)

**M 11 Feb 2019**: (Class 9)

- Quiz: Equivalence relations
- Images and preimages, right and left inverses (many examples)
- Various propositions, examples, and practice problems concerning functions
**HW**: Read textbook section 5.1 through section 5.1.4 (5 pages)

**W 13 Feb 2019**: (Class 10)

- Quiz: Functions and equivalence relations
- Relationship between functions inverses and injectivity, surjectivity, and bijectivity
- Introduction to the Principle of Mathematical Induction (textbook section 5.1.1-5.1.4)

**F 15 Feb 2019**: (Class 11)

- Collected Written Homework 1
- Quiz: Induction and Well Ordering
- More proofs by induction
- A false proof by induction (to illustrate the importance of the base case)!
- Number Theory: Properties of Divisibility (textbook section 9.1.1)

**HEADS UP: There might be some approximation error in anything labeled “Future”.**

**M 18 Feb 2019**: (Class 12–Future)

- Fibonacci numbers and relations therebetween (more induction proofs!)

**W 20 Feb 2019**: (Class 13–Future)

- The Quotient-Remainder Theorem (i.e. the Division Algorithm, i.e. textbook Theorem 9.1.4 “The Division Theorem”)
- Modular arithmetic

**F 22 Feb 2019**: (Class 14–Future)

- Minimal criminal (i.e. induction again!)
- Euclid's Lemma and the Fundamental Theorem of Arithmetic

people/grads/eppolito/math314-02-s19.txt · Last modified: 2019/02/16 08:57 by eppolito

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