347-2006-C1

Location: 143 Henry Bld
Instructor: Marius Junge Course email Office hours: Thursday 5-6pm

Book: John P. D'Angelo and Douglas West: Mathematical Thinking: Problem-Solving and Proofs, 2nd Edition

Course description : We will essentially cover chapter 1 to 8 and 13 to 15 (optimistic). Some details:

Plan:
   Introduction of the real numbers
    - motivation
    - axioms of the real numbers
    - some introduction to logic: functions and quantifiers
    - elementary inequalities
   The natural number and the induction principle
   Divisibility and modular arithmetic combined with some reasoning on cardinality
    -Prime number factorization theorem
    -q-nary expansion
    -Existence of multiplicative inverses
    -Cardinality for finite sets
    -Binomial coefficients and some combinatorics
    -Fermat's little Theorem
   The rational numbers
    - countable and uncountable sets
   Seqeunces and series
   The real numbers system
   Continuous functions

Comments: Math 347 is by no means an ordinary course! Here you may learn what mathematics is all about. You may decide to hate or love it: I hope you will love it. This is the first course where you can learn what mathematics is really about: proofs. Proofs are not a burden invented for students. Proofs create a connection between different objects in mathematics. Proofs are like the oil in the machine which make it work. Thus be prepared for an intense learning exercise. Every mathematician had to start some day learning what you will learn: the basic rules in mathematics. Ask questions! Don't think everybody knows better than you do-this feeling is common and commonly wrong. I strongly recommend study groups, in particular for your homework. Sharing your first experience in understanding proofs is really fun. Moreover, it is through explaning mathematics to to others that we really understand the stuff.