MATH 97 Variable Topics, Lecture 1
Instructor: Christian Haesemeyer
Office: MS 6304
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.
We are going to use: Courant and Robbins What is Mathematics?, 2nd Edition.
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.