Course Schedule

Course Page: http://www.math.msu.edu/~magyar/Math299 .

The dates below are tentative. Changes will be announced in class and on our course page.

Section numbers refer to:

• [H] Kevin Houston, How to Think Like a Mathematician
• [B] Matthias Beck, The Art of Proof (available online)

Lect	Date	Section: Topic
1	8/28	[H2,3,4] Reading and writing mathematics
R	8/29	Recitation
2	8/30	[H1] [B5] Sets and functions
	9/2	Labor Day, no class
3	9/4	[H1] [B5] Sets and functions; examples, models, enumeration
R	9/5	Recitation
4	9/6	[H30] [B9.1,13.1] Injective, surjective, bijective functions
5	9/9	Combinatorial enumeration & bijections
6	9/11	[B13.2-3] Cardinality, countability, Cantor's arguments
R	9/12	Recitation
7	9/13	[H30] [B9.1,13.1] [B13.4-5] Axiomatic set theory, continuum hypothesis, logical incompleteness
8	9/16	[H6] Making a statement
9	9/18	[H7] [B3.2] Implications
R	9/19	Recitation
10	9/20	[H8] [B3.2] More on implicatiions
11	9/23	[H9] [B3.3] Converse and equivalence Last day to withdraw with refund
12	9/25	[H10] [B3.1] Quantifiers: for all, there exists
R	9/26	Recitation
13	9/27	[H11,12] [B3.3] Negation of quantifiers
14	9/30	Review
15	10/2	Review
E	10/3	Midterm 1
16	10/4	[H2,14] Definitions, theorems, proofs
17	10/7	Example: divisibility of integers, infinity of primes
18	10/9	[H15, 16] Definitions, theorems
R	10/10	Recitation
19	10/11	[H17, 18] Proof example: m,n odd ⇔ mn odd
20	10/14	[H19] Pythagoras' Theorem
21	10/16	[H20] Proof by direct argument Last day to withdraw with no grade reported
R	10/17	Recitation
22	10/18	[H21,22] Common mistakes; proof by cases
23	10/21	[H23] Proof by contradiction,√2 irrational
24	10/23	[H26] Proof of contrapositive
R	10/24	Recitation
25	10/25	[H24, 25] Proof by induction
26	10/28	[H27,28] Greatest common divisor gcd(a,b), Euclidean algorithm
27	10/30	[H28] Euclidean algorithm, unique factorization thm
R	10/31	Recitation
28	11/1	[H29,31] [B6.1&3] Modular arithmetic, equvialence classes
29	11/4	[H29] [B6.3, App B] Extra: finite fields, cryptography
30	11/6	Review
E	11/7	Midterm 2
31	11/8	[B1.1-2, 8.1] Real number field
32	11/11	[B1.3, 8.2] Ordering of reals
33	11/13	[B8.3-4] Upper bounds, completeness axiom
R	11/14	Recitation
34	11/15	[B10.4] Limits
35	11/18	Intermediate value theorem?
36	11/20	Sequences & series
R	11/21	Recitation
37	11/22	More on Reals
38	11/25	[B App C.1] Complex numbers
39	11/27	[B App C.2] Complex numbers
	11/28	Thanksgiving, no recitation
	11/29	Thanksgiving, no class
40	12/2	Review
41	12/4	Review
R	12/5	Recitation
42	12/6	Review. Class moved to 1255 Anthony Hall.
E	12/9	Final exam 10:00-12:00