LIFE BEYOND CALCULUS
2006-2007 Pre-registration Information
There are several options for students
who complete a year of calculus and wish to study more mathematics. Here is a
brief description of each of the basic post-calculus courses and sequences that
will be offered in the Department of Mathematics this year. If you have further
questions, please see Diane Herrmann (office Eckhart 212; email diane@math.uchicago.edu) or John Boller (office Ryerson 352; email boller@math.uchicago.edu).
The
following courses are required by some majors; none of them may be used to
satisfy mathematics major requirements.
Math
19510-19610. This two-quarter sequence emphasizes the utility of
multivariable calculus and linear algebra in applications to the social and
biological sciences. All the basic tools of linear algebra and multivariable
calculus are introduced and are illustrated by many examples. Theoretical and
computational aspects of the subject are given equal consideration. Offered Autumn-Winter at 8:30 MWF, 11:30 MWF and 12:30 MWF. Offered
Winter-Spring 11:30 MWF and 12:30 MWF. Offered Spring-Winter 12:30 MWF.
Math
20000-20100. This analysis
sequence is designed for students intending to major in the physical sciences
(other than mathematics). Students who proceed successfully through Mathematics
20000-20100-20200 are qualified to take
Math
22000.This
course is designed for students intending to major in physics. Math 22000 is
offered in the Spring to prospective physics
concentrators who are also taking Physics 13100-13200-13300. Offered
10:30 MWF Spring.
The
following courses may all be used to fulfill mathematics major requirements.
Math
19900. This (new!!)
one-quarter course covers the fundamentals of theoretical mathematics and
prepares students for upper level mathematics courses beginning with Math
20300. This course is especially intended for students making the transition
from Math 15300 to Math 20300, or for those who need more preparation in
learning to read and write proofs. Topics include: the construction of the real
numbers, completeness and the least upper bound property, the topology of the
real line, the structure of finite-dimensional vector spaces over the real and
complex numbers. Offered Autumn, Winter, Spring at
11:30 and 12:30 MWF.
Math 20300-20400-20500. Students
who intend to concentrate in mathematics, or who require a rigorous treatment
of analysis in several dimensions, will take Mathematics 20300-20400-20500.
This sequence is the basis for all advanced courses in analysis and topology.
Here, both the theoretical and problem solving aspects of multivariable
calculus and some linear algebra are treated carefully.
NEW: This
course has a revised prerequisite of Math 16300 or Math 19900. Students must be
familiar with proof techniques using axioms for the real numbers in order to
begin this sequence. There will no
longer be separate sections of this course for students who have completed Math
15300 or Math 13300. Such students must complete Math 19900 before
registering for Math 20300. In 2006-2007 there will also be one section (31 at
10:30 MWF) for students who apply for, but do not qualify for, Honors Analysis.
Offered 10:30 MWF, 11:30 MWF and 12:30 MWF. One section of this course also
begins in the Winter Quarter.
Summary
of changes: New prerequisite for Math 20300 is Math 16300 or Math 19900. Autumn
20300 section 31 for highly qualified students not
taking honors.
Math 20700-20800-20900. This is a
highly theoretical sequence in analysis, which is reserved for the most able
students. Admission is by invitation only. Students who wish to enter this
sequence must earn high grades (A's and A-'s) in Mathematics 16100-16200-16300,
and receive a strong recommendation from the instructor in these courses.
Admission may also be gained by exceptional performance on the Calculus
Placement Test. This sequence covers the real number system, metric spaces,
basic functional analysis, the Lebesgue integral, and
other topics. Offered 10:30 MWF.
Math 25400-25500-25600. This is
the department's regular algebra sequence. Although the prerequisite is one
year of calculus, this sequence is traditionally taken by students after they
have had a sequence in analysis. Therefore, students who take algebra
immediately after calculus often find themselves less prepared for the depth of
the material than their fellow students. Two quarters of this sequence are
required of all concentrators in mathematics. Abstract linear algebra is
covered in the second quarter of the sequence. Offered 8:30 MWF and 10:30 MWF.
One section of this course also begins in the Winter Quarter, although students
should realize that the third quarter is only offered in the Spring.
Math 25700-25800-25900. This is a
highly theoretical sequence in algebra, which is intended for the most able
students. Unlike admission to Honors Analysis, admission to this sequence is by
student choice. Students who have completed Math 20700-20800-20900 should register
for section 31. Others may register for either section. Offered 10:30 MWF.