MAT 300 – Techniques of Proof
Prerequisite: MAT 161 and MAT 270
Fall 2019, MWF 12:00-12:50, Bacon 214A

Textbook Syllabus Homework
Instructor Exam Schedules
 Quiz Schedule
Internet Resourses Grades Advice for Success

MAT 270 Course Description: Topics include logic, mathematical induction, sets, relations, functions, permutations.
Textbook: A Logical Introduction to Proof  by Daniel W. Cunningham.  Errata

Preface
Table of Contents
Section 1.1 Logical Form and Logical Equivalence


Internet Resourses

Truth Table Builder
Image and Inverse Image of a Function
Euclidean Algorithm

Instructor

Professor Daniel Cunningham
Office: A255 Buckham Hall
Office Hours: W 2-3, Thur 11-1
Send Email to Me
Telephone: 878-6422 (leave message)

On Mathematical Writing

  1. On writing in Mathematics
  2. Mathematical Writing
  3. A Guide to Writing Mathematics
  4. A Primer of Mathematical Writing
Examinations: No electronic devices or notes will be allowed during in-class exams.

There will be two midterms and a final. Written exams will be graded on their content and clarity. Clear and understandable proofs are critical in this course.
  1. Exam 1: Chapters 1 and 2.  Sept. 27.  Review Problems  Cheat Sheet 
  2. Exam 2: Chapters 3 and 4.2, 4.4.  Friday Nov. 8.  Review Problems   Proofs
  3. Final Exam: Chapters 5 and 6.  Monday Dec. 9, 9:40 to 11:00.  Review Problems  Some Proofs
Homework
  1. Exercises 1.1: 1, 2, 3, 4, 5, 6.
  2. Exercises 1.2: 1, 2, 3, 4, 5 
  3. Exercises 1.3: 2.     
  4. Exercises 2.1: 1, 2, 3, 5. 
  5. Exercises 2.2: 2, 3, 4, 5, 6.  Figure 2.1
  6. Exercises 2.3: 1, 3, 4.  
  7. Exercises 2.4: 1, 3, 5, 6.  
  8. Exercises 2.5: 1, 2, 3. 
  9. Exercises 3.1: 2, 7, 8, 9, 10, 15, 19. 
  10. Exercises 3.3: 2, 3, 5, 7.  
  11. Exercises 3.4: 1–13 odds.  
  12. Exercises 3.5: 1–7.
  13. Exercises 3.6: 2, 3, 4, 9, 11. 
  14. Exercises 3.7: 3, 7.  
  15. Exercises 3.8: 14, 16, 19. 
  16. Exercises 4.1: 4, 5.  
  17. Exercises 4.2: 1, 2, 6.  
  18. Exercises 4.4: 1, 4, 8, 9.  Write each proof by induction in the same format as the proof of Theorem 4.2.2 of the text.  In your proof DO NOT use the notation P(1), P(n), or P(n + 1).
  19. Exercises 5.1: 2, 3, 8, 11.
  20. Exercises 5.2: 1, 2, 4, 5.
  21. Exercises 5.3: 9(a), 9(d), 9(f).    Unions and Intersections
  22. Exercises 6.1: 1, 2, 3, 4.
  23. Exercises 6.2: 5, 6, 8, 14, 15.  
  24. Exercises 6.3: 3, 6, 9, 10. For 10, apply proof strategy 6.1.10. 
  25. Exercises 6.4: 3, 7, 9, 12.
  26. Exercises 7.1: 3, 4, 6, 7.
  27. Exercises 7.2: 2, 5, 8.
Homework Quiz Schedule
  1. Exercises 1.2 – Friday, Sept. 6
  2. Exercises 2.2 – Friday, Sept. 13
  3. Exercises 2.3, 2.4, 2.5 – Friday, Sept. 20
  4. Exercises 3.1, 3.3 – Friday, Oct. 4
  5. Exercises 3.4, 3.5 –  Friday, Oct. 11
  6. Exercises 3.6, 3.7, 3.8 – Friday, Oct. 18
  7. Exercises 4.2 – Friday, Oct. 25
  8. Exercises 4.4 – Friday, Nov. 1
  9. Exercises 5.1, 5.2, 5.3 – Friday, Nov. 15.
  10. Exercises 6.1 – Friday, Nov. 22.
  11. Exercises 6.2 – Friday, 
  12. Exercises 6.3, 6.4 – Wednesday,
Advice for Success

Former students who have done well in this course recommend the following advice:
Grades

A link to your exam grades, listed under your Secret ID, is available Here.