Math 310 Spring,
2012
Dept. of Mathematics Washington Univ.
Syllabus for Math 310
Foundations
for Higher Mathematics
Instructor: Steven G. Krantz
e-mail address: sk@math.wustl.edu
Office: 103, Cupples I
Office
Hour: MWF 12:00pm-1:00pm
Phone: (314) 935-6712
Dept.
Office: 100 Cupples I
Dept.
Phone: (314)
935-6760
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,
2nd edition, CRC Press, Boca Raton,
FL, 2002.
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.
All homework assignments are taken from The Elements of Advanced Mathematics , second edition ( not the first or third edition).
First Homework Assignment:
pages 21-25: #1.1bdfh, 1.2bdfh, 1.3bdfh, 1.4bdfh, 1.5bdfh, 1.6bdfh, 1.10bdfh, 1.12, 1.14bdf, 1.18
Due Friday, January 27, 2012, in class.
Second Homework Assignment
pages 43-46: #2.1, 2.3, 2.9, 2.10, 2.21, 2.23, 2.24, 2.25, 2.28, 2.29, 2.34, 2.39
Due Friday, February 3, 2012, in class.
Third Homework Assignment
pages 57-59: #3.1bdf, 3.3bdg, 3.4b, 3.5ace, 3.7, 3.10, 3.12, 3.15, 3.18bdhj, 3.21ab, 3.28, 3.29
Due Friday, February 10, in class.
Fourth Homework Assignment
pages 85-90: #4.1, 4.5, 4.8, 4.9bdf, 4.10bdfh, 4.11, 4.15, 4.18, 4.20bdfhj, 4.23, 4.25bdf, 4.28
Due Friday, February 24 in class.
Fifth Homework Assignment
pages 101-103, #5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.16, 5.18, 5.22, 5.26, 5.27
Due Wednesday, March 21 in class.
The First Midterm Exam will be Monday, March 5 in class. It will cover Chapters 1 to 4 of the text. There will be about ten questions.
Sixth Homework Assignment
pages 141-145, #6.4, 6.5, 6.8, 6.11, 6.13, 6.17, 6.21, 6.29, 6.31, 6.33, 6.39, 6.45
Due Friday, April 6, in class.
No class on Friday, March 30. Have a good rest.
Seventh Homework Assignment
pages 156-158, #7.3, 7.4, 7.6, 7.9, 7.11, 7.14, 7.16, 7.25, 7.26, 7.27
Due Wednesday, April 18, 2012 in class.
The Second Midterm Exam will be on April 20, 2012 in class. It will cover Chapters 5 and 6 in the text. Of course it should be understood that the material in Chapters 5 and 6 relies in essential ways on the earlier material.
There will be no class on Friday, April 13 (Friday the thirteenth is bad luck anyway).
Eighth Homework Assignment
pages 180-183, #8.2, 8.5, 8.9, 8.10, 8.12, 8.13, 8.14, 8.21, 8.23, 8.24
Due Friday, April 27, 2012 in class.
The Final Exam is Wednesday, May 9 from 1:00pm to 3:00pm in Brown 118.