| MTH 299 | Transition to Formal Mathematics | Fall 2013 |
Course Page: http://math.msu.edu/~duncan42/Fall13S5.html.
The dates below are tentative. Changes will be announced in class and on our course page.
Section numbers refer to:
| 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
| E | 12/9 | Final exam 10:00-12:00
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