# Math 300 - Introduction to Abstract Mathematics - Fall 2004

### Handouts, Resources, Etc:

 Class Schedule Class Date Material Assignment 1 W Aug 18 Class Intro; Fundamentals of Mathematics Read pp 1-8 2 F Aug 20 Immersion! Field Axioms (Chapter 5) Read pp 58-60 HW 1: #1, 2, 3 from Problems #1, expand (x+1)(x+2) listing all the axioms used 3 M Aug 23 More Field Axiom work; quantifiers HW 2: #4, 5, 14 from Problems #1, Quantifier Handout (pdf) 4 W Aug 25 More Field Axiom work; negation HW 3: #8, 12 from Problems #1, Negate Quantifier Practice #2-5 5 F Aug 27 Order Axioms New Axiom List HW 4: #20, 21, 24, 26, 29 6 M Aug 30 Integer Powers; Notebook Info HW 5: #31, 34, 38 7 W Sep 1 Proofs with Quantifiers HW: do and bid on undone problems in range #1-37 8 F Sep 3 Problems & Review HW 6: #41, 42, Essay Proof Problems (PDF) M Sep 6 Labor Day Holiday 9 W Sep 8 Absolute Value HW 7: #46, 47, 52, 53, 58 (new problem sheet avail at top) New HW Policy: HW due class period after next (today's due Monday) 10 F Sep 10 More Absolute Value HW 8: #55, 61, 63 (due Wed) 11 M Sep 13 Set Theory HW 9: #65, 66, 71, 73, 75 (new problem sheet (#4) avail) 12 W Sep 15 More Set Theory (Complement & Reflection) HW10: #67, 68, 69, 80, 84 (due Wed) 13 F Sep 17 Exam Preview; More Set Theory (Venn Diagrams); Updated version of Problems Sheet #4 available No Homework - Study 14 M Sep 20 Exam #1 on material thru Absolute Value 15 W Sep 22 More Set Stuff HW11: #110, 111, 112, 113, 115, 116 16 F Sep 24 Return Exam; Functions (Chapter 3) HW12: #92, 99, 101, 102, 104 (rest of problems from #4 are available for bidding) 17 M Sep 27 More Functions HW13: #119, 120, 129, 150, 151, 154 (new problem sheet) 18 W Sep 29 Inverse Functions; 1-1 and Onto HW14: #131 132, 156, 160, 163 19 F Oct 1 More 1-1 and Onto HW15: from book: #8efg (pg. 38), from prob sheet: #135, 138, 166 20 M Oct 4 Real functions: domain, range, odd and even HW16: from book: #12def (pg. 40), from prob sheet: #123, 125, 142 21 W Oct 6 Review of Sets & Functions Homework Holiday: all current HW (15, 16) due on Monday, also work on Bid problems 22 F Oct 8 Sets, Functions & Infinity HW17: from today's handout: #2, #9 23 M Oct 11 Cartesian Products and Relations (Chapter 2) HW18: from new prob sheet: #168, 180, 182, 171, 173 (due Monday!) 24 W Oct 13 Exam Review No Homework F Oct 15 Fall Break 25 M Oct 18 Exam #2 on Sets and Functions 26 W Oct 20 Relations: Reflexive, Symmetric, Transitive HW19: #174, 184bce 27 F Oct 22 Equivalence Relations HW20: #185bdh 28 M Oct 25 (Abstract) Equivalence Relations & Partitions HW21: #188, 191, 192 Correct Missed Problems on Exam (due Friday) Update to Notebook Problem List; First check Mon Nov 1: Armistead thru McGill 29 W Oct 27 Wrap-up Equivalence Relations; Begin Induction (Ch. 4) HW22: #185fg (also determine the partition defined by the equivalence classes), #190 30 F Oct 29 Induction: Intro & Sums HW23: #194, 196, 198 (new problem sheet) 31 M Nov 1 Induction: Divisibility HW24: #201, 204, 209 32 W Nov 3 Induction: Variations HW25: #202, 212, 213 33 F Nov 5 Induction: Inequalities HW26: #219, 225, 235 (new problem sheet) Notebooks for 2nd half of class due Monday 34 M Nov 8 Induction: Inequalities HW27: #223, 226, 227 35 W Nov 10 Induction: Inequalities HW28: #228, 233, 236 36 F Nov 12 Induction: Recursion HW29: #241, 244, 246 Notebooks for 1st half of class due Monday 37 M Nov 15 Review; Induction: Recursion HW30: #248, #250 38 W Nov 17 Exam #3 on Relations and Induction (thru Inequalities) Problems #167 thru 239 39 F Nov 19 Induction: Binomial Formula HW31: #252, 253, 254, 256, 261 40 M Nov 22 Induction: Binomial Formula HW32: #262, 263, 265 41 W Nov 24 Lots of Bid Problems! No HW F Nov 26 Thanksgiving Holiday 42 M Nov 29 Course Summary & Final Overview Notebooks due by Friday 3PM for the check that counts Th Dec 9 Final Exam, 8:00-10:00AM

ccollins@math.utk.edu