## Math 300A, Autumn 2017 - Homework Assignments

 Wk. Reading Practice Problems Hand-In Problems Due Date 1 Note to Students, §1.1 & 2.1; 1st two pages of Axioms for the Real Numbers See this pdf. See this (same) pdf. W 10/4 2 Finish reading Ch. 2 and Axioms for the Real Numbers §2.1, pp.40-42: 2,9cd; §2.2, pp.49-51: 3abcd,10 §2.3, pp.61-62: *ed if need practice; §2.1, pp.40-42: 3E,8,9,12 §2.2, p.51: 3fhgi,12abcfg; §2.3, p.62: 4c,5b; Give a 2C proof of Theorem 41; see link below for "Rules for Citing Reasons") W 10/11 3 § 2.1, Ch. 3 §1.2, pp. 26-27: 1,2,3; §2.4, pp.74-77: 3ace,10a; §3.1, p.96: 1; §3.2, p.112: 1,3. §1.2, pp. 26-28: 4c,7P/CE §2.4, pp.74-77: 3bdg,10bc; §3.1, pp.96-101: 3ac,19ab; §3.2, p.112: 5. W 10/18 4 Review Chapter 3 and Homework guidelines; Read Appendix A, pp. 492-496. Optional additional writing guidance: Remarks on Writing Mathematical Proofs §3.1, p.96: 3b §3.3, pp.126-127: 6ab §3.1, pp.100-101: 19cd §3.2, p.113: 11 §3.3, pp.126-127: 6cd,7 §3.4, p.138: 5,7 W 10/25 5 §§4.1-4.2 Optional: Mathematical Induction, Proofs of the principle of math induction and variations §3.3, p.127: 9P/CE; §3.5, pp.153-154: 6,7,13; §4.1, p.180: 3a. §3.3, p.130: 20c; §3.4, pp.139-140: 12bc,13a; §3.5, pp.153-154: 8ab,11a,12; §4.1, p.180: 3bc. W 11/1 6 §§5.1-5.3 none Corrected Portfolio Problem. W 11/8 7 Chapter 5 §4.1, p.182: 11ab; §4.2, p. 196: 4abc; §5.1, pp. 225-226: 5,7ck, rest of 7 if needed; §5.2, pp. 240-241: 7,15ab. §4.1 p.182: 2 proofs for 11c, inductive and not; §4.2, p. 196: 1c,4d; §5.1, pp. 227-228: 12ef,14; §5.2, pp. 239-241: 2b,15d. W 11/15 8 Start Chapter 6 §5.4 p. 262: 1&2 if needed; §5.5, pp. 274-275: 3ab,12a. Portfolio P. final submission. §5.3, pp. 252-253: 5; 11a by set algebra; §5.4 pp. 262-263: 5,8,9; in 8, is either implication true if A is empty? §5.5, pp. 274-275: 3cd, 10, 12c. W 11/22 9 §§6.1-6.4,6.6 Inverse Functions (replaces §6.5) §6.1, pp.292-293: 6,7abc; §6.2, p. 303: 1,3cd,4a §6.3, pp. 318-319: 2,9 §6.4, pp.331-332: 4a,7abf Hotel Infinity Brain Teasers §6.1, p.293: 7defgh - change h to consider only finite sets T; §6.2, p. 303: 4bc §6.3, pp. 317-319: 1,6,8 §6.4. pp.331-332: 4b,6,7cdeh W 11/29 10 Chapter 9; recommended reading after §9.1: More about finite sets, and after §9.2: More about countable sets. §6.6, pp.358-359: 5,6,10,11; pp. 476-477, Preview Activity 1: be prepared to play "Dodge Ball" and win. §6.4, p.333: 10b; §6.6, pp.358-359: 7,8,9,13; Review: §3.5, p.155: 16. W 12/6
E = Give explanation (doesn't have to be formal proof.)
2C = Give 2-Column proof.
P/CE = Give proof or counterexample.

Homework guidelines.
Rules for Citing Reasons in Proofs in homework.