Department of Mathematics

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.

 

 

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.

 

 

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.