M201C: Introduction to proofs

Mathematics 201C: Introduction to Proofs

Instructor: Jonathan Smith, 496 Carver, 4-8172 (voice mail)

e-mail: jdhsmithATiastateDOTedu (substitute punctuation)

Office Hours: Mon. 2.10 - 4 pm, 5.15 - 6.05 pm; Wed. 12 - 12.50 pm (subject to change). Also Mon., 5/5, 2.10-4pm.

Grading: 80% for in-class assignments (at random times), homework (last assignment due 4/28), and class participation; 20% for the final (Tue., 5/6, 9.45 - 11.45 am).
Click here for information about special accommodations.

Click here for tally of points earned.

Textbooks:

(BP) R. Hammack, Book of Proof, 2nd. ed. ISBN 978-0-9894721-0-4.
(BA) J. Lebl, Basic Analysis: Introduction to Real Analysis.

Study Plan: Regular attendance and participation in class activities are the prerequisites for success. Except in extreme circumstances, no accommodation can be given for failure to meet this responsibility.

Assignments will be given regularly. They will not be graded each week, but it is absolutely essential to solve each homework problem in order to understand the material and develop the necessary skills.

Communication devices must remain switched off during the class periods and final.

Syllabus: Sets, logic, proofs in algebra and calculus.

Assignments

Click here for Practice Final in PDF

4/28 for 4/30: Read (BA) Sections 3.2.1-3; do (BA) Exercises 3.2: 1, 3, 5 (prove continuity at x=0), (p.108).

Click here for the Third Graded Homework in Portable Document Format (due 4/28).

4/25 for 4/28: Read (BA) Sections 2.5.1-3; do (BA) Exercises 2.5: 1, 2, 3(a)(b)(d) (p.81).

4/23 for 4/25: Read (BA) Section 2.4; do (BA) Exercises 2.4: 1, 2, 4, 5 (p.71).

4/21 for 4/23: Read (BA) Sections 2.3.1-2; do (BA) Exercises 2.3: 1, 2, 5, 6 (p.67).

4/18 for 4/21: Read (BA) Section 2.2.1 and Prop. 2.2.5; do (BA) Exercises 2.2: 1, 2, 3, 5, 7 (p.60).

4/16 for 4/18: Complete reading of (BA) Section 2.1; do (BA) Exercises 2.1: 3, 4, 13, 14, 15, 17 (pp.49-50).

Click here for Practice Test #2 in Portable Document Format

4/9 for 4/11: Read (BA) Section 2.1 through Section 2.1.1; do (BA) Exercises 2.1: 1, 2, 9, 10 (pp.49-50).

4/7 for 4/9: Read (BA) Section 1.3; do (BA) Exercises 1.3: 1, 2, 3, 5 (p.34).

4/4 for 4/7: Read (BA) Section 1.2.2; do (BA) Exercises 1.2: 1, 2, 8 (p.30).

4/2 for 4/4: Read (BA) Sections 1.1, 1.2.1 (not proof of Ex. 1.2.3), 1.2.3, 1.2.4; do (BA) Exercises 1.1: 2, 4, 6, 9 (p.24); Exercises 1.2: 4, 9 (p.30).

3/31 for 4/2: Read (BP) Section 13.3; do the Second Graded Homework.

3/28 for 3/31: Read (BP) Sections 13.1, 13.2; do (BP) Exercises 13.2: 2, 4, 6, 8 (p.226).

3/26 for 3/28: 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, 10 (p.220).

3/24 for 3/26: 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).

3/14 for 3/24: 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).

3/10 for 3/12: Do (BP) Exercises 10: 20, 34 (pp.168-9), using induction or otherwise.

3/7 for 3/10: Read (BP) Sections 10.1, 10.2; do (BP) Exercises 10: 10, 18, 22, 24 (pp.167-8), using induction or otherwise.

3/5 for 3/7: Read (BP) Chapter 10 through p.158; do (BP) Exercises 10: 2, 4, 6, 8, 16 (pp.167-8), using induction or otherwise.

3/3 for 3/5: Read (BP) Section 3.4; do (BP) Exercises 3.4: 2, 4, 8, 10, 12 (p.78).

Click here for Practice Test #1 in Portable Document Format

2/24 for 2/26: Read (BP) Chapter 9; do (BP) Exercises 9: 4, 12, 16, 28, 30, 34 (p.151).

2/21 for 2/24: Read (BP) Sections 8.1, 8.2; do (BP) Exercises 8: 4, 6, 8, 20, 22 (p.143).

2/19 for 2/21: Read (BP) Chapter 7; do (BP) Exercises 7: 2, 4, 12, 18, 20 (p.127).

First graded homework (due 2/19)

For each question, state the proposition and write a formal proof.

(3 points.) If x is an integer, then x² + 5x +6 is even.
(3 points.) If x is an integer, and x² + 4 is odd, then x is odd.
(3 points.) There are no integers x, y
such that 6x + 9y = 1.

Click here for printable version.

2/14 for 2/17: Read (BP) Sections 6.1, 6.2; do (BP) Exercises 6: 2, 6, 8, 10 (p.116).

2/12 for 2/14: Read (BP) Sections 5.1, 5.3; do (BP) Exercises 5: 2, 4, 6, 12, 16 (p.108).

2/10 for 2/12: Read (BP) Sections 4.4, 4.5; do (BP) Exercises 4: 14, 16, 18, 20, 26 (pp.98-9).

2/7 for 2/10: Read (BP) Sections 4.1 to 4.3; do (BP) Exercises 4: 2, 4, 6, 10, 12 (p.98).

2/3 for 2/5: Read (BP) Section 2.10; do (BP) Exercises 2.10: 2, 4, 6, 8 (pp.58-9).

1/31 for 2/3: 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).

1/29 for 1/31: Read (BP) Sections 2.5, 2.6; do (BP) Exercises 2.5: 10 (p.46); 2.6: 6, 8, 12, 14 (p.49).

1/27 for 1/29: Read (BP) Sections 2.3, 2.4; do (BP) Exercises 2.3: 2, 4, 8, 10 (p.42); 2.4: 2, 4 (p.44).

1/22 for 1/24: Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10. (p.39).

1/17 for 1/22: Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 6, 9, 14 (p.27).

1/15 for 1/17: 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).

1/13 for 1/15: 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).