MATH 109 : Mathematical Reasoning (Winter 2016)

Instructor: Alvaro Pelayo,

Office Hours: Tu 2:30pm-3:30pm and Th 12:30pm-1:30pm, APM 7444

Course Assistants:
Susan Elle, (office hours: M 1pm-2pm, F 3pm-4pm)
Joseph Palmer, (office hours: M F 11am-1pm)

Meetings: TuTh 11:00am-12:20pm, room CSB 001

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 Thursday January 28, 2016 (25%), Midterm Exam 2 on Thursday February 25, 2016 (25%), cumulative Final Exam (35%) on Thursday March 17, 2016. Exams will consist of a few theory questions, including definitions and proofs, and some problems involving computations and proofs. All exams are closed book and closed notes, no calculators or electronic devices are allowed. 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. Homework must be placed before 4:00pm on the due date in the drop-box in the basement of APM. No late homework is accepted and the two lowest homework grades will be dropped (which can also count for missing assignments).

Prerequisites: Math 20F or Math 31AH 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' book and not all sections will be covered in the same depth. Class time is for the fundamental concepts of each chapter. Eccles' book (and also the other books) are sources for further explanations and examples. The following is an approximate plan. Content covered will be added/updated below as the course progresses (numbers refer to sections in Eccles' book).


Lecture 1 (Tu January 5): Section 1 Homework 1 (due Monday January 11)

Lecture 2 (Th January 7): Section 2


Lecture 3 (Tu January 12): Section 3 Homework 2 (due Tuesday January 19)

Lecture 4 (Th January 14): Section 4, Section 5


Lecture 5 (Tu January 19): Section 6 Homework 3 (due Monday January 25)

Lecture 6 (Th January 21): Section 6


Lecture 7 (Tu January 26): Section 7 Homework 4 (due Monday February 8)

Lecture 8 (Th January 28): Midterm Exam 1


Lecture 9 (Tu February 2): Section 8

Lecture 10 (Th February 4): Section 9


Lecture 11 (Tu February 9): Section 9, Section 10 Homework 5 (due Tuesday February 16)

Lecture 12 (Th February 11): Section 10


Lecture 13 (Tu February 16): Section 10 Homework 6 (due Monday February 22)

Lecture 14 (Th February 18): Section 11


Lecture 15 (Tu February 23): Section 12

Lecture 16 (Th February 25): Midterm Exam 2


Lecture 17 (Tu March 1): Section 12

Lecture 18 (Th March 3): Introduction to Diophantine Equations Homework 7 (due Friday March 11)

WEEK 10:

Lecture 19 (Tu March 1): Section 14

Lecture 20 (Th March 3): Section 14 and Review