TR 3:55 p.m.-5:10 p.m. BLOC 148
Math 300 is designed to provide a bridge between computational mathematics and theoretical mathematics (``real math''). Thus a major goal is to teach the students how to write proofs.
The required core of topics include logic, set theory, number theory, induction, functions, relations, operations, and combinatorics.
Tamara J. Lakins,
, 1st edition, American Mathematical Society, Pure and applied undergraduate texts, The Sally Series.
| Date of Class |
Material covered |
| Thursday 08/25 |
general introduction, statements, predicates, logical connectives and-or-not
|
| Tuesday 08/30 |
DeMorgan's laws, logical equivalence, implication |
| Thursday 09/01 |
Quiz #1 , logical connectives: converse, contrapositive, biconditional. Quantifiers: existential and universal quantifiers, membership. |
| Tuesday 09/06 |
Quantifiers: rules of negation. Proof techniques: Modus Ponens, Modus Tollens. |
| Thursday 09/08 |
Quiz #2 , Proof techniques: proof of existential statements, proof of uniqueness in existential statements.
|
| Tuesday 09/13 |
proofs of universal statements |
| Thursday 09/15 |
Quiz #3 , disproving universal statements, proof by contrapositive |
| Tuesday 09/20 |
proof by contradiction |
| Thursday 09/22 |
Quiz #4 , other proof techniques |
| Tuesday 10/27 |
review for Exam 1 |
| Thursday 10/29 |
Exam #1 (covers sections 1.1-2.3) |
| Tuesday 10/04 |
principle of mathematical induction |
| Thursday 10/06 |
Quiz #5 , principle of strong mathematical induction |
| Tuesday 10/11 |
Fall Break, no classes |
| Thursday 10/13 |
Quiz #6 , sets, emptyset, subsets, equality |
| Tuesday 10/18 |
unions, intersections |
| Thursday 10/20 |
Quiz #7 , complements, DeMorgan Laws |
| Tuesday 10/25 |
arbitrary unions, arbitrary intersections |
| Thursday 10/27 |
Quiz #8 , power set, cartesian product |
| Tuesday 11/01 |
review for Exam 2 |
| Thursday 11/03 |
Exam #2 (covers induction and set theory) |
| Tuesday 11/08 |
equivalence relations |
| Thursday 11/10 |
Quiz #9 functions |
| Tuesday 11/15 |
injectivity, surjectivity, bijectivity of functions |
| Thursday 11/17 |
Quiz #10 , composition, invertibility |
| Tuesday 11/22 |
invertibility and bijectivity |
| Thursday 11/24 |
Thanksgiving, reading day, no classes |
| Tuesday 11/29 |
Functions and sets: direct and inverse images |
| Thursday 12/01 |
Quiz #11 , introduction to cardinal theory, review for the final |
| Tuesday 12/06 |
Fall redefined day, class canceled |
| Thursday 12/08 |
reading day, no classes |
| Tuesday 12/13 |
Final exam (covers relations and functions) |