Math 310, Spring, 2016

Dept. of Mathematics, Washington Univ.

**Syllabus
for Math 310**

Foundations for Higher Mathematics

**Instructor:**
Steven G. Krantz

**Classroom:**
Hillman 60

**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,*

3rd edition, CRC Press, Boca Raton,
FL, 2012.

**Elements
of the Course:**

Homework: 20% of grade

Midterm Exam: (2 of these) each 20% of grade

Final Exam: 40% 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 **

pages 22-28: 1bdg, 2bfj, 3dfh, 4bfj, 5dfh, 6bdf, 10bd, 13dhj

Assigment due Friday, January 29, 2016 in class.

** Second Homework Assignment **

pages 52-56: 1, 3, 4, 9, 12, 14, 17, 20, 24, 25, 29, 34, 42, 44

Assigment due Wednesday, February 10, 2016 in class.

** Third Homework Assignment **

pages 68-72: 1bdf, 3bdf, 4b, 5bd, 7, 10, 13, 15, 18bfjk, 21b, 27

Assignment due Wednesday, February 17, 2016 in class.

The First Midterm will be on Wednesday, February 24 in class.

It will cover Chapters 1 through 3 in the text. There

will be a review session for the exam on Monday, February 22.

Also the Department has posted old exams on the departmental

Web site, which is http://www.math.wustl.edu.

** Fourth Homework Assignment **

pages 99-107: 3, 6, 9bdf, 10bdf, 11, 15, 20cdfh, 25bd, 28, 34, 42

Assignment due Friday, March 4, 2016 in class.

** Fifth Homework Assignment **

pages 123-125: 1, 2, 5, 7, 10, 14, 17, 18, 22, 27, 28abc

Assignment due Wednesday, March 23, 2016 in class.

** Sixth Homework Assignment **

pages 166-173: 4, 6, 8, 10, 17, 18, 21, 24, 25, 28, 29, 31, 32, 43

Assignment due Monday, April 4, 2016 in class.

**
The Second Midterm Exam, covering Chapters 4, 5, 6, will
be held on April 8, 2016 in class.
**

Here is a sketch of what will happen for the rest of the semester:

a) Today, March 30, we will finish covering Chapter 6 of the text.

b) On Friday, April 1, we will go over homework 6 (which is due Monday)
and cover a couple of "extra topics" which will not be on the test.

c) On Monday, April 4 we will hand in Homework 6 and
we will review for Midterm 2.

d) On Wednesday, April 6 we will have no class but instead I will
have an office hour from 11:00am until 2:00pm in my office (103, Cupples I).

e) On Friday, April 8 we will have Midterm 2 in class. It will cover
Chapters 4, 5, 6.

f) On Monday, April 11 we will take the day off.

g) For the remainder of the semester, beginning Wednesday, April 13,
we will cover Chapters 7 and 11 to the extent that time permits.

** Seventh Homework Assignment **

pages 185-188: 1, 2, 3, 5, 6, 12, 16, 17, 20, 21, 26, 27

Assignment due Monday, April 25, 2016 in class.

** Eighth Homework Assignment **

pages 269-274: 1, 2, 4, 10, 12, 13, 23

Assignment due Friday, April 29, 2016 in class.

Extra Office Hours to prepare for the Final Exam:

Thursday, May 5: 3:30pm - 5:30pm

Monday, May 9: 2:00pm - 4:00pm

Tuesday, May 10: 3:30pm - 5:30pm

**
The Final Exam will be on May 11 from 1:00pm
to 3:00pm in Hillman 60 (our usual classroom).
**

**
You may bring two 4" x 6" notecards to the exam, written on both
sides.
**