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

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

**
Course Assistants:**

Susan Elle, selle@ucsd.edu (office hours: M 1pm-2pm, F 3pm-4pm)

Joseph Palmer, j5palmer@ucsd.edu (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).

**WEEK 1**:

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

Lecture 2 (Th January 7): Section 2

**WEEK 2**:

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

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

**WEEK 3**:

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

Lecture 6 (Th January 21): Section 6

**WEEK 4**:

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

Lecture 8 (Th January 28): ** Midterm Exam 1 **

**WEEK 5**:

Lecture 9 (Tu February 2): Section 8

Lecture 10 (Th February 4): Section 9

**WEEK 6**:

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

Lecture 12 (Th February 11): Section 10

**WEEK 7**:

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

Lecture 14 (Th February 18): Section 11

**WEEK 8**:

Lecture 15 (Tu February 23): Section 12

Lecture 16 (Th February 25): Midterm Exam 2

**WEEK 9**:

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