Lectures:

• MWF 10:30-11:20 am in Porter Hall room A20
• MWF 1:30-2:20 pm in Wean Hall room 6423

Problem seminar: Meets most Thursdays at 7:30pm in Wean Hall 5320. First meeting is Jan. 24.

• Problem batch 1
• Problem batch 2
• Problem batch 3
• Problem batch 4
• Problem batch 5
• Problem batch 6

Instructors: Dhruv Mubayi

• Office: 6307 Wean Hall
• Phone: (412)268-9865
• email: mubayi AT cmu.edu
• Office hours: to be arranged

• Office: 6130 Wean Hall
• Phone: (412)268-2553
• email: rpego AT cmu.edu
• Office hours: MW 2:30, T 3:30, and by arrangement

Analysis assignments:

• analysis assignment 1, due M 1/28: pdf
• analysis assignment 2, due F 2/22: pdf
• analysis assignment 3, due W 4/2: pdf
• analysis assignment 4, due W 4/30: pdf

Algebra assignments

• Proof that e is transcendental pdf

Texts:

• Abstract Algebra by I. Herstein,
• Real Mathematical Analysis by C. Pugh, published by Springer.

• Functions of Several Variables by Wendell Fleming, published by Addison-Wesley.
• Calculus on Manifolds by Michael Spivak, published by Benjamin.
• Differential Forms and Applications by Manfredo P. do Carmo, published by Springer.
• Topics in Algebra by I. Herstein, published by Xerox Publishing.

Course Description:   This semester will focus on:

• Multivariable differential calculus (Pugh, sections 5.1-5.7)
• Integration in n dimensions;
Differential forms, Stokes theorem (Pugh, 5.8-5.10)
• Rings, Fields, Linear algebra
• Further topics to be determined

Grading:   Based on

• One mid-term test,
• Homework,
• Problem seminar presentations and a small group project report
• Final exam.

Tests: There will be one midterm take-home test during the semester, with two parts, to be taken between Friday, February 29 and Monday, March 3

Homework PDF files will be emailed or posted online at http://www.math.cmu.edu/~bobpego/21236/ . This is the most important part of the course. Homework solutions 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 and small group projects: This term the problem seminar format will be arranged to encourage everyone to participate and practice presentation skills. Different problems will be assigned to small groups (of 2 or 3) which are responsible for solving the problem and giving a polished presentation to the seminar. We expect to alternate weeks in the seminar between working on the problems in small groups some weeks, and having groups present solutions the next week. Groups will later work on a (more substantial) small project that will involve writing a report and giving a presentation in seminar.

Final Exam: There will be a mandatory comprehensive final examination; this will be take-home.

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.

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.

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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