M201A: Introduction to proofs

Mathematics 201A: Introduction to Proofs

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

e-mail: jdhsmithATiastateDOTedu (substitute punctuation)

Office Hours: Mon. 10am, 11 am, 3.10 pm; Wed., Fri. 10am (subject to change). Also Mon., 12/15, 1.30-3.30pm.

Click here for Math Help Room (385 Carver) Math 201 times.

Grading: 80% for in-class assignments (at random times), homework (last assignment due 12/8), and class participation; 20% for the final (Tue., 12/16, 7.30-9.30am).

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 the Practice Final in Portable Document Format.

Click here for the Third Graded Homework in Portable Document Format (due 12/8).

12/5 for 12/8: Read (BA) Sections 2.5.3, 2.5.5; do (BA) Exercises 2.5: 3(a), (b) (p.81).

12/3 for 12/5: Read (BA) Sections 2.5.1-2; do (BA) Exercises 2.5: 1, 2, 3(d) (p.81).

12/1 for 12/3: Read (BA) Section 2.4; do (BA) Exercises 2.4: 1, 2, 4, 5 (p.71).

11/21 for 12/1: Read (BA) Sections 3.2.1-3; do (BA) Exercises 3.2: 1, 3, 5 (prove continuity at x=0), (p.108).

11/19 for 11/21: Read (BA) Section 2.2.1 and Prop. 2.2.5; do (BA) Exercises 2.2: 1, 2, 3, 5, 7 (p.60).

Click here for Practice Test #2 in Portable Document Format

11/12 for 11/14: Complete reading of (BA) Section 2.1; do (BA) Exercises 2.1: 3, 4, 13, 14, 15, 17 (pp.49-50).

11/10 for 11/12: Read (BA) Section 2.1 through Section 2.1.1; do (BA) Exercises 2.1: 1, 2, 9, 10 (pp.49-50).

11/7 for 11/10: Read (BA) Section 1.3; do (BA) Exercises 1.3: 1, 2, 3, 5 (p.34).

11/5 for 11/7: Read (BA) Section 1.2.2; do (BA) Exercises 1.2: 1, 2, 8 (p.30).

11/3 for 11/5: 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).

10/31 for 11/3: Read (BP) Section 13.3; do the Second Graded Homework.

10/29 for 10/31: Read (BP) Sections 13.1, 13.2; do (BP) Exercises 13.2: 2, 4, 6, 8 (p.226).

10/27 for 10/29: 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).

10/24 for 10/27: 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).

10/22 for 10/24: 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).

10/17 for 10/20: Do (BP) Exercises 10: 20, 34 (pp.168-9), using induction or otherwise.

10/15 for 10/17: Read (BP) Sections 10.1, 10.2; do (BP) Exercises 10: 10, 18, 22, 24 (pp.167-8), using induction or otherwise.

10/13 for 10/15: Read (BP) Chapter 10 through p.158; do (BP) Exercises 10: 2, 4, 6, 8, 16 (pp.167-8), using induction or otherwise.

10/10 for 10/13: 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

10/3 for 10/6: Read (BP) Chapter 9; do (BP) Exercises 9: 4, 12, 16, 28, 30, 34 (p.151).

10/1 for 10/3: Read (BP) Sections 8.1 to 8.3; do (BP) Exercises 8: 4, 6, 8, 20, 22 (p.143).

9/29 for 10/1: Read (BP) Chapter 7; do (BP) Exercises 7: 2, 4, 12, 18, 20 (p.127).

First graded homework (due 9/29)

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

(4 points.) If x is an integer, then x² - 3x + 1 is odd.
(4 points.) If x is an integer, and x² - 2 is odd, then x is odd.

Click here for printable version.

9/26 for 9/29: Read (BP) Sections 6.1, 6.2; do (BP) Exercises 6: 2, 6, 8, 10 (p.116).

9/24 for 9/26: Read (BP) Sections 5.1, 5.3; do (BP) Exercises 5: 2, 4, 6, 12, 16 (p.108).

9/22 for 9/24: Read (BP) Sections 4.4, 4.5; do (BP) Exercises 4: 14, 16, 18, 20, 26 (pp.98-9).

9/19 for 9/22: Read (BP) Sections 4.1 to 4.3; do (BP) Exercises 4: 2, 4, 6, 10, 12 (p.98).

9/15 for 9/17: Read (BP) Section 2.10; do (BP) Exercises 2.10: 2, 4, 6, 8 (pp.58-9).

9/12 for 9/15: 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).

9/10 for 9/12: Read (BP) Sections 2.5, 2.6; do (BP) Exercises 2.5: 10 (p.46); 2.6: 6, 8, 12, 14 (p.49).

9/8 for 9/10: Read (BP) Sections 2.3, 2.4; do (BP) Exercises 2.3: 2, 4, 8, 10 (p.42); 2.4: 2, 4 (p.44).

9/5 for 9/8: Read (BP) Sections 2.1, 2.2; do (BP) Exercises 2.2: 1, 3-5, 7-10. (p.39).

8/29 for 9/3: Read (BP) Section 1.8; do (BP) Exercises 1.8: 2, 6, 9, 14 (p.27).

8/27 for 8/29: 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).

8/25 for 8/27: 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).