Honors Mathematics I:
Professor Karen E. Smith
Course assistant: Ruthi Hortsch
Intended audience: super smart, hardworking freshman who want to see some honest theoretical mathematics
Course Objective: To introduce students to the art and practice of mathematics while redeveloping the calculus of one variable rigorously on firm mathematical ground.
Prerequisites: AB Calculus.
Text: Spivak, Calculus, Edition 4.
Some topics we will cover: fields, ordered fields, the real numbers, least upper bounds, limits, elementary point set topology including abstract topological spaces, continuity, compactness and connectedness (mainly in the real numbers), intermediate value theorem, uniform continuity, integration, differentiation, chain rule, fundamental theorem of calculus, taylor polynomials.
Details about course organization on the Math 295 Course Information Sheet
A list of topics and assignments given each day on the Daily update, in addition to the weekly problem sets.
New! Lecture Notes on Topology Lectures typed up by John Holler: October 25 , October 26 , October 27 , October 29 , November 1 , November 2 , November 3 , November 5
John's Write up of the CHAIN RULE lecture: Chain Rule
John's Write up of the (first) CANTOR FUNCTION lecture: Cantor Function
Problem Sets: Set 1 , Set 2 , Set 3 , Set 4 , Exam I Problems , Set 5 , Set 6 , Set 7 , Set 8 , Exam II Problems , Set 9 , Set 10 , Final Exam Problems.
Handouts: Handout 1 on Notation and Logic, Handout 2 on How to write proofs , Handout 2A on Absolute Value , Handout 3 on Induction , Handout 4 on the Division Algorithm and digit expansion , Handout 5 summarizing definitions not found in text , Handout 6 discussing Closed sets in the real number line ,
Practice Sheet , Logic Practice Sheet
Some statistics and Commentary on Exam I Results
Some statistics and Commentary on Exam II Results