Math 310, Fall, 2018

Dept. of Mathematics, Washington Univ.

**Syllabus
for Math 310**

Foundations for Higher Mathematics

**Instructor:**
Steven G. Krantz

**Classroom:**
Busch 100

**e-mail
address:** sk@math.wustl.edu

**Office:**
103, Cupples I

**Office
Hour: **MWF, 2:00pm-3:00pm.

**Phone:**
(314) 935-6712

**Dept.
Office:** 100, Cupples I

**Dept.
Phone:** (314) 935-6760

**Course Home
Page:** http://www.math.wustl.edu/~sk/math310.html

**Course
Description:** The purpose of this course is

to serve as a transition between
calculation-oriented courses

like calculus and differential equations and more
theoretical

courses like analysis and abstract algebra. Math 310
covers

logic, set theory, proofs, number systems, axiomatics, and

other aspects of mathematical rigor. Group theory,

non-Euclidean geometry, and basic real analysis

are offered as illustrations of the ideas in the course..

**Textbook:**
S. G. Krantz, *The** Elements of
Advanced Mathematics,*

4th edition, CRC Press, Boca Raton,
FL, 2017.

**Elements
of the Course:**

Homework: 25% of grade

Midterm Exam: (3 of these) each 25% of grade

TOTAL: 100%

The homework is an essential part of this course.
Each new idea

builds
on previous ideas, so it is essential to master and internalize each

one
when you encounter it. Be sure to do the homework in a regular and timely

fashion. Homework should
be written out on 8.5" x 11" paper and submitted

on time. It will be graded..

Be familiar with this Web page. This is where homework assignments will be
posted, homework

solutions posted, exam solutions posted, due dates will be posted,

and also where exams and other course events
and information

will be announced.

FIRST HOMEWORK ASSIGNMENT

Due Monday, September 10 in class.

pages 26-33, # 1bd, 2bf, 3bd, 4df, 5bf, 6bd, 9bd, 10bf, 13bf, 17

SECOND HOMEWORK ASSIGNMENT

Due Friday, September 21 in class.

pages 60-65, # 3, 6, 9, 10, 14, 20, 22, 24, 28, 31, 34, 35, 37

The first midterm exam will be on Monday, October 1, 2018. It will
be in class: from 1:00pm to 2:00pm in Busch 100. You may bring
a pencil and 4 x 6 card with notes. No calculators or computers.

THIRD HOMEWORK ASSIGNMENT

Due Monday, October 8 in class.

pages 79-83, #1efg, 3bd, 4a, 5bd, 7, 9, 11, 12, 15, 18bdfk, 26

Here is our plan of action for the next few days:

Friday, September 28: Review for exam in class

Monday, October 1: First Midterm Exam in class

Wednesday, October 3: No class

Friday, October 5: Class as usual

FOURTH HOMEWORK ASSIGNMENT

Due Monday, October 22 in class.

pages 119-127, #1, 3, 5, 9ace, 10ace, 11, 17, 18, 20abefhm, 25abe

FIFTH HOMEWORK ASSIGNMENT

Due Friday, November 2 in class.

pages 146-149, #1, 4, 6, 7, 16, 18, 21, 23, 27, 28ade

SIXTH HOMEWORK ASSIGNMENT

Due Monday, November 12 in class.

pages 198-207, #1, 3, 4, 6, 9, 11, 15, 17, 21, 29, 31, 33, 43, 53

SEVENTH HOMEWORK ASSIGNMENT

Due Monday, December 3 in class.

pages 220-223, #1, 2, 5, 6, 9, 12, 16, 19, 21, 26