MATH 109 : Mathematical Reasoning (Fall 2014)

Instructor: Alvaro Pelayo,

Office Hours: M 1:10-2pm, F 12:10-1pm APM 7444

Course Assistant: Joseph Palmer,

Meetings: MWF 11-11:50am, room CSB 002

Required Text: Peter J. Eccles, "An Introduction to Mathematical Reasoning", Cambridge University Press, 1997.

Other texts:

Rod Haggerty, "Fundamentals of Mathematical Analysis", Addison-Wesley Second Edition 1993

David M. Burton, "Elementary Number Theory", Allyn and Bacon 1976

Keith Devlin, "Sets, functions and logic, an introduction to advanced mathematics", Princeton University Press, 1993

Daniel J. Velleman, "How to prove it, a structured approach", Cambridge University Press 1994

Grading: homework (15%), Midterm Exam 1 on Friday October 31, 2014 (25%), Midterm Exam 2 on Monday November 24, 2014 (25%), cumulative Final Exam (35%) on December 16, 2014. Exams will consist of a few theory questions, including definitions and proofs of selected results, and some problems involving computations and proofs. There will be no make-up exams - if you miss one midterm, the final exam counts 60%. If you take both midterms and your grade in the final is greater than your lowest midterm grade, then the grade in the midterm gets replaced by the grade in the final. For example, if midterm 1 score is 80/100, midterm 2 score is 50/100 and final score is 70/100, your score in the second midterm gets replaced by 70/100. If you choose to be graded "Pass/Fail", a "Pass" grade reqires a grade of C- or higher.

Homework: Assignments can be downloaded from this website, no paper copy will be given in class. A grader will grade selected problems. Discussing homework with others is ok. It is expected that everyone writes in his/her own words the homework solutions. No late homework is accepted and the two lowest homework grades will be dropped (which can also count for missing assignments). Homework must be placed before 4:00pm on the due date in the drop-box in the basement of APM.

Prerequisites: Math 20F or Math 31AH (not concurrent), or consent of instructor.

Syllabus (approximate): "This course uses a variety of topics in mathematics to introduce the students to rigorous mathematical proof, emphasizing quantifiers, induction, negation, proof by contradiction, naive set theory, equivalence relations and epsilon-delta proofs" - as in (parts of) chapters 1-22 of the book.

Tentative course content: we will cover parts of Eccles' book. There will be no time to cover all of the sections in each chapter of Eccles's book and not all sections will be covered in the same depth. Class time is for the fundamental concepts of each chapter. Eccles's book (and also the other books) are sources for further explanations and examples. Content covered will be added below as the course progresses (numbers refer to sections in Eccles' book).


Lecture 1 (Fr October 3): Section 1


Lecture 2 (Mo October 6): Section 2

Lecture 3 (We October 8): Section 3 Homework 1 (due Monday October 13)

Lecture 4 (Fr October 10): Section 4 Homework 2 (due Thursday October 16)


Lecture 5 (Mo October 13): Section 5

Lecture 6 (We October 15): Section 5

Lecture 7 (Fr October 17): Section 6 Homework 3 (due Thursday October 23)


Lecture 8 (Mo October 20): Section 6

Lecture 9 (We October 22): Section 7

Lecture 10 (Fr October 24): Section 8


Lecture 11 (Mo October 27): Section 9

Lecture 12 (We October 29): Review Problems

Lecture 13 (Fr October 31): Midterm Exam 1


Lecture 14 (Mo November 3): Correction of Midterm Exam 1

Lecture 15 (We November 5): Section 10

Lecture 16 (Fr November 7): Section 10 Homework 4 (due Thursday November 13)


Lecture 17 (Mo November 10): Section 10, Section 11

Lecture 18 (We November 12): Section 11

Lecture 19 (Fr November 14): Section 12


Lecture 20 (Mo November 17): Section 12

Lecture 21 (We November 19): Section 12

Lecture 22 (Fr November 21): Section 14, review problems


Lecture 23 (Mo November 24): Midterm Exam 2

Lecture 24 (We November 26): Section 14

No Lecture (Fr November 28): No Class

WEEK 10:

Lecture 25 (Mo December 1): Homework 5 (due Thursday December 4)

Lecture 26 (We December 3): review problems

Lecture 27 (Fr December 5): Section 15, review problems

WEEK 11:

Lecture 28 (Mo December 8): Homework 6 (due Thursday December 11)

Lecture 29 (We December 10):

Lecture 30 (Fr December 12):