Mat 362 Spring 2015 Homepage

MAT 362: Differential Geometry of Surfaces

Spring 2015

ANNOUNCEMENTS:
As you all know, we are transitioning to the DoCarmo text, listed below, in place of the Petersen text, effective the week of February 16.

In the Petersen text, be familiar with the material covered to date, that is Chapter 4.1, 4.2, 4.4 and 4.5 Beyond that, you can read and learn from this text as you wish.

In the DoCarmo text, we begin with Chapter 2. We have covered much of this already in class. You'll need to know more or less the full chapter, except 2.7 and 2.8. (However, it is good to know the fact stated in the first paragraph of 2.7 - you don't need to pay attention to the proof unless you want to).
Read Ch. 2.6 (Orientability) from DoCarmo text. We won't have time to discuss in much detail in class.

HW #3, due Feb. 24, will be from DoCarmo text, and stay that way from now on, unless specifically indicated otherwise.

Midterm Exam, Tuesday March 24, 1:00-2:20pm, in class.
Material on the Midterm: All topics we've covered in class and DoCarmo, up to and including Ch. 4.2. So Chapters 2, 3 and 4.2. You may skip 2.7. 2.8 and most of 2.6 as well as 3.5A and 3.4 (although you should know basic facts about vector fields). There will be about 5 or so problems on the exam, covering roughly equally all the work done so far in the class.
The exam is OPEN BOOK. You may use any source material you like during the exam.

The FINAL EXAM will be a TAKE HOME EXAM. It will be handed out during class on Thursday, May 7, and due one week later:

TAKE HOME FINAL EXAM, DUE THURSDAY, MAY 14, 2:30PM
The exam will also be available online, here, on Thursday afternoon, May 7.
The PDF of the Final Exam is now here.

You may place the exam under my office door, Math Tower 4-110, any time before May 14, 2:30, or hand it to me in person at that time.
The exam is OPEN BOOK and OPEN SOURCE, so you may use any written or internet sources to assist you. However, you may not consult with anyone else, whether other students taking the class or anyone else, regarding the problems on the exam. All of the work on the exam, in totality from beginning to the end when you hand it in, must be fully your own work.
The exam covers the full semester of material we have covered. There will be an emphasis on topics covered since the Midterm Exam, but there will be some problems also from the first half of the semester.
Some problems will be relatively easy and straightforward, some basic computations, while some will be more difficult and challenging. The problems will mainly be "problem solving", but there will also be some "proofs" on the exam.

Instructor. Michael Anderson, Math Tower 4-110.
E-mail: anderson AT math.sunysb.edu, Phone: 632-8269.
Lectures: Tu/Th: 1:00-2:20pm, in Earth and Space Bldg. 183
Office Hours. MW 1:30-3pm, and by appointment.

Grader. Yuhan Sun, Math Tower MLC: S-240.
E-mail: yuhansun AT math.sunysb.edu
Office Hours. MW, 1-2pm in MLC, S-240A, M, 4-5pm

Course Description. The foundation of differential geometry is the concept of curvature. The course will focus on understanding this and related concepts very clearly, both geometrically and computationally, for the case of surfaces in Euclidean space. For this, you'll need a solid background in multivariable calculus and linear algebra. We hope to give some idea of how curvature is understood in higher dimensions; this is the basis of Riemannian geometry and General Relativity.

Prerequisites. MAT 205 (Calc III) and MAT 210 (Linear Algebra).

Text. The text for the class is

Manfredo do Carmo, Differential Geometry of Curves and Surfaces, Prentice-Hall, (1976).

There are a number of other reasonable texts, all with advantages and disadvantages. Among these are:

P. Petersen, Classical Differential Geometry. The link to this text is here.
Differential Geometry: A First Course in Curves and Surfaces, by T. Shifrin. Available free online: here
Curves and Surfaces, Lecture Notes for Geometry I, by Henrik Schlichtkrull, available as PDF here
Andrew Pressley, Elementary Differential Geometry, Springer Verlag, 2001.
B. O'Neill, Elementary Differential Geometry.
Millman and Parker, Elements of Differential Geometry.

The last three and many others are in the Library (I believe).

Assignments and Grading. There will be one Midterm Exam, in class:

MIDTERM: Date: Tuesday, March 24, 1:00-2:20, in class

Next, the FINAL EXAM
The FINAL EXAM will be a TAKE HOME EXAM. See the Announcements Section above for further details.

There will be regular homework assignments, due roughly once per week. Your grade will be determined via the following percentages:

Homework: 40%
Midterm: 25%
Final: 35%

Week of	Topics	Problems Due	Due Date
Jan 26	Intro (after snow day)	---	---
Feb 2	4.1 4.2	4.1: 1(a), 2(a), 10, 11 4.2: 2, 3(a)-(b)	Feb 10
Feb 9	4.4 4.5	4.4: 1, 2, 3, 5, 9 4.5: 4, 9, 16	Feb 17
Feb 16	2.5 3.1, 3.2	2.4: 1, 7, 8 2.5: 3, 14 3.2: 8	Feb 24
Feb 23	3.2 3.3	3.2: 17 3.3: 1, 5abc, 13, 16, 17	Mar 3
Mar 2	3.3, 3.5B 4.2	3.3: 22 3.5: 12, 13 4.2: 4, 7, 11	Mar 10
Mar 9	4.3 4.4	Prepare for Midterm	---
Mar 16	Spring Break	----	---
Mar 23	Midterm Exam, 4.3	4.3: 1, 2, 3, 4, 6, 8	March 31
Mar 30	4.4	4.4: 1, 4, 9, 12, 13.	Apr 7
Apr 6	4.4 4.6	4.4: 15, 22 4.6: (3, 4, 5,) 14	Apr 14
Apr 13	4.6 5.3,5.4	4.6: 3, 4, 5, 6 4.7: 1, 2(a),(c) 5.4: 4(a),(b)	Apr 21
Apr 20	5.3 4.5	5.3: 2, 3, 4, 5, 6, 8, 9	Apr 28
Apr 27	4.5	4.5: 1, 2, 3, 4	May 5

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