MATH 109 : Mathematical Reasoning (Winter 2015)


Instructor: Alvaro Pelayo, alpelayo@math.ucsd.edu

Office Hours: Tu 11-12:50pm APM 7444

Course Assistant: Joseph Palmer, j5palmer@ucsd.edu

Meetings: TuTh 9:30am-10:50am, room PETER 104

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 29, 2015 (25%), Midterm Exam 2 on Thursday February 26, 2014 (25%), cumulative Final Exam (35%) on March 17, 2015. Exams will consist of a few theory questions, including definitions and proofs, 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).


WEEK 1:

Lecture 1 (Tu January 6): Section 1

Lecture 2 (Th January 8): Section 2

WEEK 2:

Lecture 3 (Tu January 13): Section 3 Homework 1 (due Tuesday January 20)

Lecture 4 (Th January 15): Section 4, Section 5

WEEK 3:

Lecture 5 (Tu January 20): Section 6 Homework 2 (due Monday January 26)

Lecture 6 (Th January 22): Section 6

WEEK 4:

Lecture 7 (Tu January 27): Section 7

Lecture 8 (Th January 29): No lecture, Midterm Exam 1 instead

WEEK 5:

Lecture 8 (Tu February 3): Section 8 Homework 3 (due Monday February 9)

Lecture 9 (Th February 5): Section 9

WEEK 6:

Lecture 10 (Tu February 10): Section 9

Lecture 11 (Th February 12): Section 10 Homework 4 (due Tuesday February 17)

WEEK 7:

Lecture 12 (Tu February 17): Section 10

Lecture 13 (Th February 19): Section 11 Homework 5 (due Tuesday February 24)

WEEK 8:

Lecture 14 (Tu February 24): Section 11

Lecture 15 (Th February 26): No lecture, Midterm Exam 2 instead

WEEK 9:

Lecture 16 (Tu March 3): Section 12

Lecture 17 (Th March 5): Section 12 Homework 6 (due Friday March 13)