Lectures:

• MWF 10:30-11:20 am in Doherty Hall room 1211
• MWF 1:30-2:20 pm in Scaife Hall room 220

Problem seminar: TBA

Instructors: James Cummings

• Office: Wean Hall 7101
• Phone: (412)268-2551
• email: jcumming AT andrew.cmu.edu
• Office hours: by appointment

• Office: Wean Hall 6130
• Phone: (412)268-2553
• email: rpego AT cmu.edu
• Office hours: 4-5:30 TTh or by appointment

Algebra Assignments

• Due Wednesday 9/1: tex   pdf
• Due Wednesday 9/8: tex   pdf
• Due Wednesday 9/15: tex   pdf
• Due Wednesday 10/13:   pdf
• Due Wednesday 10/27:   pdf
• Due Wednesday 11/17:   tex   pdf

Analysis Assignments

• Due Friday 9/3: pdf
• Due Friday 9/10: pdf
• Due Friday 9/17: pdf
• Due Friday 10/8: pdf
• Due Friday 10/22: pdf
• Due Friday 11/19: pdf

Handouts/Links:

• On total disconnectedness pdf
• The logical chain reaction (aka mathematical induction) pdf

• Mind:  Forget What You Know About Good Study Habits (NY Times)
• How to teach arithmetic? (BBC)
• Plus magazine
• Math Matters

• Abstract Algebra, by D. S. Dummit and R. M. Foote, published by Wiley.
• Real Mathematical Analysis, by C. Pugh, published by Springer.
  

• Topics in Algebra, by I. Herstein, published by Wiley.
• Principles of Mathematical Analysis, by W. Rudin, published by McGraw-Hill.

• How to Prove It: A Structured Approach by D. J. Velleman, Cambridge Univ. Press.
• What is Mathematics, Really by Reuben Hersh, Oxford Univ. Press.

Course Description:   This semester will focus on:

• Nature of the real numbers, Rⁿ, cardinality
• Metric space topology (Pugh, ch. 3)
• Function spaces (Pugh, ch. 4)
• Group theory (Dummit and Foote, Part I)
• Rings and fields
• Vector spaces and linear algebra

Workload This is a 20 unit course, which nominally means that you should expect to spend 20 hours per week on the material - 7 in class attendance and participation and about double that outside of class, studying, writing and being stuck! This is probably realistic.

Grading:   Based on

• Two mid-term tests,
• Homework,
• Problem seminar presentations and write-ups,
• Final exam.

Tests: There will be two tests during the semester, each with two parts. The first test will be held in class, part 1 on Wednesday, Sept. 22, part 2 on Friday, Sept. 24. The second test will be take-home, during the period November 1-3.

Homework is normally due weekly. PDF files for analysis will be posted online at http://www.math.cmu.edu/~bobpego/21235/ . This is the most important part of the course. Homework solutions should be written up carefully in grammatical English. They will be graded both for content and quality of presentation. An important objective of the course is mastery of presentation of mathematical material.

Problem seminar problems: These are normally to be presented two weeks after they are assigned, with a preliminary discussion in the problem seminar the week before presentations. Further details to be announced.

Final Exam: There will be a mandatory comprehensive final examination; this will be take-home, with rules that will be explained nearer that time.

Make-up tests are only possible in the case of a documented medical excuse, a university-sanctioned absence (e.g., participation in a varsity sporting event), or a family emergency. Please contact us at the earliest time possible to schedule a make-up.

Collaboration Students are strongly encouraged to discuss homework and problems with others and consult other resources to improve their understanding. Academic integrity, however, requires that your tests, written homework solutions, and problem seminar write-ups are your independent work and not copied from other sources. Homework solutions from previous semesters, if available, cannot be used. When you use someone else's ideas, you should cite that source (people or publications) clearly and indicate at which steps of a solution you have used each source.

Remarks

• Attendance and participation in class is important. We will not be following the texts exactly; material will be included and excluded freely and handouts may be used.
• The material will be presented in a formal and abstract way. It is easy to believe that you understand because it seems logical in class, but this is usually a complete illusion. You must re-process the material by reformulating it in your own terms and working examples and problems. This is best done after each class, on a regular basis. Last-minute thinking on the day before assignments are due or tests are given will not be sufficient to succeed.

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