### Math 347 - Honors section

### Time/Location: MWF, 1-1.50 pm, 343 Altgeld Hall

### Instructor: Marius Junge, Altgeld
363, Office hour, TBA

**Texts: Mathematical Thinking, D'Angelo and West, Prentice Hall **

Grading:
Homework (30%), Midterm: (40%), Final (30%), Class discussion (10%) -to improve your grade by substitution.

Outline:

The
course Math 347 is an intermideate course, between more calculus
style math classes, and more prove oriented classes such as real
analysis and linear algebra. The aim of this course is to cover basic
principles of logic, reasoning, proof writing and finding, and real
content. In this honors section it is expected that you are willing to
work on your one and on a team.

We will cover certain topics, and the descritiption below covers the key words. You are expectet to attend the class and deepen you knowldege by reading on your own.

Topics:

1) Basics:
Functions, sets, logical statements, quantifiers, relations, some
graphs, induction and cardinality, axioms for rings, fields, and
completeness axiom (definition). This corresponds to part I in
D'Angelo-West.

2) Numbers: Equivlence
classes, building the rationals from the integers, Grothendieck group,
modular arithematic, Fermat's Little Theorem, Rational and irrational
numbers, extening rational by adding solutions.

3) Combinatorics and probability: Arrangments
and selections, binomial theorems, discrete probability spaces,
conditional expectation and expectation. random variables, Pigeon
principles, Graphs including coloring problems.

4) Continuous math: Completeness
axiom and applications, limits and convergence, Cauchy sequences,
continuity (sequence and epsilon delta), monotone squences and
subsequences, differentiation and integration (only if time permits).

Homework: See Box folder