### 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