Math 2010 – Introduction to Proofs

Course coordinator

Jonathan Smith
jdhsmith@iastate.edu
515-294-8172

Catalog description

MATH 2010: Introduction to Proofs
(3-0) Cr. 3. F.S.

Prereq: MATH 1660 or MATH 166H
Transition to advanced mathematics. Communicating mathematics. Logical arguments; techniques of proofs regarding sets, numbers (natural and real), functions, relations, and limits.

Textbook

Book of Proof

Hammack
ISBN: 9780989472128

Basic Analysis I
Lebl
ISBN: 9781718862401

Syllabus

Sets, logic, proofs in algebra and calculus.

Objectives

This class is designed to guide students through the transition from example-based calculus courses to advanced proof-based classes in mathematics. Emphasis is placed on learning how to recognize and handle valid mathematical statements, to create proofs of true statements, and to disprove false statements. A second objective is to learn how to communicate mathematics effectively, both in written and spoken form. Thus it should be appreciated, for example, that a string of disconnected statements cannot constitute a valid argument. Proof-writing should be recognized as an art, where the level of detail to be included in the proof of a statement has to be matched to the level of that statement and to the intended audience.

Sample assignments

Random quizzes are not included in this list.
Practice exams may be assigned in advance as preparation for in-class tests and the final.

Read (BP) Sections 1.1, 1.2; do (BP) Exercises 1.1: 1-4, 17-20, 30-33, 39, 41, 43 (p.7); 1.2:1, 3, 10, 12, 20 (p.10).

Read (BP) Sections 1.3 to 1.7; do (BP) Exercises 1.3: 2, 4, 10 (p.14); 1.4: 4, 5 (p.16); 1.5:2(a)-(c), 4(f)(g)(h) (p.18); 1.6: 2(a),(f),(g) (p.20); 1.7: 10, 12 (p.23).

Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 6, 9, 14 (p.27).

Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10. (p.39).

Read (BP) Sections 2.3, 2.4; do (BP) Exercises 2.3: 2, 4, 8, 10 (p.42); 2.4: 2, 4 (p.44).

Read (BP) Sections 2.5, 2.6; do (BP) Exercises 2.5: 10 (p.46); 2.6: 6, 8, 12, 14 (p.49).

Read (BP) Sections 2.7 to 2.9; do (BP) Exercises 2.7: 4, 8, 10 (p.51); 2.9: 2, 4, 6, 10 (p.55).

Read (BP) Section 2.10; do (BP) Exercises 2.10: 2, 4, 6, 8 (pp.58-9).

Read (BP) Sections 4.1 to 4.3; do (BP) Exercises 4: 2, 4, 6, 10, 12 (p.98).

Read (BP) Sections 4.4, 4.5; do (BP) Exercises 4: 14, 16, 18, 20, 26 (pp.98-9).

Read (BP) Sections 5.1, 5.3; do (BP) Exercises 5: 2, 4, 6, 12, 16 (p.108).

First Graded Homework

Read (BP) Sections 6.1, 6.2; do (BP) Exercises 6: 2, 6, 8, 10 (p.116).

Read (BP) Chapter 7; do (BP) Exercises 7: 2, 4, 12, 18, 20 (p.127).

Read (BP) Sections 8.1 to 8.3; do (BP) Exercises 8: 4, 6, 8, 20, 22 (p.143).

Read (BP) Chapter 9; do (BP) Exercises 9: 4, 12, 16, 28, 30, 34 (p.151).

Test #1.

Read (BP) Section 3.4; do (BP) Exercises 3.4: 2, 4, 8, 10, 12 (p.78).

Read (BP) Chapter 10 through p.158; do (BP) Exercises 10: 2, 4, 6, 8, 16 (pp.167-8), usinginduction or otherwise.

Read (BP) Section 10.1; do (BP) Exercises 10: 10, 18, 22, 24 (pp.167-8), using induction orotherwise.

Read (BP) Sections 11.0, 12.1; do (BP) Exercises 11.0: 2, 4, 12, 14 (p.176); 12.1: 2, 4, 8, 10(pp.198-199).

Read (BP) Sections 12.2, 12.4, 12.6; do (BP) Exercises 12.2: 2, 4 (p.202); 12.4: 2, 6(p.208); 12.6: 2, 6 (p.214).

Read (BP) Sections 12.5, 13.1 (through Theorem 13.1); do (BP) Exercises 12.2: 9, 10(p.202); 12.5: 2, 6 (p.212); 13.1: 4, 6, 8 (p.220).

Read (BP) Sections 13.1, 13.2; do (BP) Exercises 13.2: 2, 4, 6, 8 (p.226).

Second Graded Homework.

Read (BA) Section 1.1; do (BA) Exercises 1.1: 1, 2, 4, 6, 9 (p.24).

Read (BA) Sections 1.2.1 (not proof of Ex. 1.2.3), 1.2.3, 1.2.4; do (BA) Exercises 1.2: 4, 7,9 (p.30).

Read (BA) Section 1.2.2; do (BA) Exercises 1.2: 1, 2, 8 (p.30).

Read (BA) Section 1.3; do (BA) Exercises 1.3: 1, 2, 3, 5 (p.34).

Read (BA) Section 2.1 through Section 2.1.1; do (BA) Exercises 2.1: 1, 2, 9, 10 (pp.49-50).

Test #2.

Complete reading of (BA) Section 2.1; do (BA) Exercises 2.1: 3, 4, 13, 14, 15, 17 (pp.49-50).

Read (BA) Section 2.2.1 and Prop. 2.2.5; do (BA) Exercises 2.2: 1, 2, 3, 5, 7 (p.60).

Read (BA) Sections 3.2.1-3; do (BA) Exercises 3.2: 1, 3, 5 (prove continuity at x = 0),(p.108).

Read (BA) Section 2.4; do (BA) Exercises 2.4: 1, 4, 5 (p.71).

Read (BA) Sections 2.5.1-3; do (BA) Exercises 2.5: 1, 2, 3(b)(d) (p.81).

Third Graded Homework.

Read (BA) Prop. 2.5.14.

Final.

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