Math 310, Spring, 2020

Dept. of Mathematics, Washington Univ.

**Syllabus
for Math 310**

Foundations for Higher Mathematics

**Instructor:**
Steven G. Krantz

**Classroom:**
TBA

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

**Office:**
103, Cupples I

**Office
Hour: **Monday, Wednesday, Friday from 10:30am to 11:30am.

**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: (2 of these) each 25% of grade

Final Exam: 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.

We will decide when our midterm exams will be. They will be in class.
If there are particular days when you do not want an exam (for a religious
holiday or other reason), please let me know.

FIRST HOMEWORK ASSIGNMENT due Monday, January 27 in class.

pages 26-33

1. acg

2. bdf

4. bdf

5. bdf

6. bd

10. bdf

14. bdf

22.

SECOND HOMEWORK ASSIGNMENT due Friday, February 7 in class.

pages 60-65

1, 3, 12, 13, 17, 20, 24, 28, 34, 35, 37, 42, 44

THIRD HOMEWORK ASSIGNMENT due Friday, February 21 in class.

pages 79-83

1bcf, 2, 3bdf, 5bdf, 7, 10, 11, 13, 16, 18aefin

pages 119-127

1, 3, 9bdf, 10bdfh, 11

FOURTH HOMEWORK ASSIGNMENT due Monday, March 2 in class.

pages 119-127

17, 18, 19, 20acfhil, 24, 28, 34, 42, 47

FIFTH HOMEWORK ASSIGNMENT due Monday, March 30 by 10:00pm on CrowdMark.

pages 146-149

#1, 4, 7, 8, 17, 18, 22, 25, 27

pages 198-207

#1, 3, 4, 5, 6, 9

SIXTH HOMEWORK ASSIGNMENT due Wednesday, April 8 by 10:00pm on CrowdMark.

Chapter 6 Exercises:

#11, 15, 17, 23, 27, 29, 39, 40, 43, 45

SEVENTH HOMEWORK ASSIGNMENT due Friday, April 17 by 10:00pm on CrowdMark.

Chapter 7 Exercises:

#1, 2, 3, 9, 11, 16, 19, 21

Chapter 8 Exercises:

#2, 4, 17, 21

EIGHTH HOMEWORK ASSIGNMENT due Friday, April 24 by 10:00pm on CrowdMark.

Chapter 8 Exercises:

#30, 31, 33

Chapter 11 Exercises:

#1, 2, 4, 10, 12, 23