**MATH 97 Variable Topics, Lecture 1**
**Instructor:** Christian Haesemeyer
**Office: MS 6304**
**phone:** 310-825-3364
**Office hours:**M:10:00-11:00 W:4-5 F:1-2

**Teaching Assistant:**Siddarth Bhaskar

**Time and Location:**
MWF 2pm, MS 6201 (Lectures)*and* T 2pm, MS 5138 (Discussion section).

**Syllabus and assignments:**
Week 1: Natural numbers. Principle of induction. (Pages 9-21 of the book.)
Homework 1, due October 1st.
Week 2: Number bases. Equivalence relations.
Homework 2, due October 8th.
Week 3: Modular arithmetic, Euclidean algorithm, Fundamental theorem of arithmetic. (Pages 21-51 of the book.)
Homework 3, due October 15th.
Week 4: Rational and irrational numbers, construction of the real numbers. (Pages 52-72 of the book.)
Homework 4, due October 22nd.
Week 5: Sequences and limits. (Pages 289-299 of the book.)
Takehome midterm exam: to be returend at the beginning of class October 27th.
Week 6: Monotone sequences, continuous functions, the Bolzano-Weierstrass theorem. (Pages 312-327 of the book.)
Homework 5, due November 5th.
Week 7: Polynomials. Algebraic and transcendental numbers.
Homework 6, due November 12th.
Week 8: Complex numbers. De Moivre formula. The Fundamental Theorem of Algebra. (Pages 88-103 of the book.)
Homework 7, due November 19th.
Week 9: Finite, countable, uncountable sets. Uncountability of the reals.
Homework 8, due November 29th.
Week 10: Schroeder-Bernstein theorem. Existence of transcendental numbers. (Pages 77-88 of the book.)
Final Exam. To be turned in no later than Wednesday, December 8th.

**Literature:**
We are going to use: Courant and Robbins *What is Mathematics?*, 2nd Edition.

**Grading Policy:**

There will be 9 homework assignments, to be handed in in class on Fridays. Late homework will not be accepted; the lowest score will be dropped. There will also be one midterm exam, and a final exam. Make-up exams will not be given. Grading will be based on the better of (a) Homework 25%, Midterm 25% amd Final 50%, or (b) Homework 25% and Final 75%. This class will use the myUCLA gradebook facility.

Requests for a regrading will only be considered within 14 calendar days of the due date of the original assignment, and no later than the day before the final. All such requests *must* be directed to the instructor; the TA is not allowed to make changes to grades.