Math 310, Spring, 2016

Dept. of Mathematics, Washington Univ.

Syllabus for Math 310

Foundations for Higher Mathematics

Instructor: Steven G. Krantz

Classroom: Hillman 60

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 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:

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

#### Solutions to First Homework Assignment

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.

#### Solutions to Second Homework Assignment

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.

#### Solutions to First Midterm

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.

#### Solutions to Homework 5

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.

#### Solutions to Midterm 2

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.

#### Solutions to Final Exam

Eighth Homework Assignment

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

Assignment due Friday, April 29, 2016 in class.

#### Solutions to Homework 8

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.