Draft of August 15 , 2002

Prerequisites: 2 quarters of calculus

Part-time options? No. (Register for 16 credits)

Schedule: Tuesday, Thursday, Friday 1 – 6:30 p.m.

• First meeting: Tuesday, October 1, 2002 in room 2242 of Lab II at 1 p.m.
• PLEASE NOTE: TEXTS WILL COST over $500 AND MUST BE PURCHASED BY THE SECOND DAY OF CLASS. MY PREVIOUS EXPERIENCE IS THAT THOSE WHO DO NOT PURCHASE THE TEXTS BY THE SECOND DAY OF THE QUARTER END UP DROPPING THE PROGRAM. (We will use these texts all year, so the book costs for winter and spring will be under $200, I think.) Do not buy texts without the student solutions manual (and Mathematica guides). These will come "bundled" with texts purchased at our bookstore, THEY WILL NOT BE AVAILABLE FOR SEPARATE PURCHASE THROUGH OUR BOOKSTORE! BE SURE to get the correct edition of the texts if you buy them somewhere besides our bookstore. Don’t buy the seminar books until you get to campus and be sure to get the same edition that everyone else gets so that we all have the same page numbers to refer to in the seminar. I’ll list the approximate prices of the texts through the bookstore, but they could be a bit less.

2.  Mathematica Computer Guide for Kreyszig's AEM  (bundled with above text using the ISBN above)

3.  Student Solutions Manual for Kreszig's AEM (bundled with above text using the ISBN above)

4.  Differential Equations, 2nd edition by Blanchard, Devaney, Hall, pub. Brooks/Cole 0-534-67428-3
This is a "bundled" ISBN including the student man. below. $126 at bookstore (approx.)

5. Student Solutions Manual for Differential Equations by Blanchard , pub. Brooks/Cole  (bundled with ISBN above)

6. The Joy of Mathematica, 2nd edition by Shuchat and Shultz $60 retail (bookstore?), Harcourt Academic Press 0-12-640730-4

7.  The Mystery of the Aleph by Aczel $15 (approx.) Pocket Books 0743422996  (paper) 

8.  Chaos by Gleick, Penguin 0140092501 $13

9.  Introduction to Linear Algebra, FIFTH edition by Johnson, Riess, Arnold $118 (approx.) Addison Wesley 032114340x)
This is a "bundled" ISBN including the student solutions manual below.

10.  Student Solutions Manual for Linear Algebra text above by Camp, pub. Addison Wesley (included with the bundled ISBN above)

11. Subscriptions and Membership in the Mathematical Association of America
Information on 1^st day of class. Purchase by 2^nd day of class $30

TOTAL $528 + tax

Remember, this is approximate!

useful for work in mathematics: Schaum’s Mathematical Handbook
 

Schedule:		FALL	WINTER	SPRING
Tuesday 1- 6:30 p.m.		Ordinary  Differential  Equations	Nonlinear  Differential  Equations	Partial Differential  Equations
Thursday 1 – 6:30 p.m.		Computer Lab  A. Applications for  Differential Equations & Linear Algebra B. Mathematica	Differential  Geometry	Projects
Friday 1 – 6:30 p.m.		Linear Algebra	Linear Algebra (1st half of quarter)  Differential  Geometry  (2nd half of quarter)	Differential  Geometry  includes  Calculus of Variations

 

Changes from the catalog: I wrote the catalog copy well over a year ago and since that time, I have had discussions with colleagues at Evergreen and other colleges about the content of the program. After these discussions, I have decided that we should replace Functional Analysis and Number Theory with Differential Geometry. Differential Geometry is an upper division class at all universities and it will be more theoretical than other portions of the program, but I’ve chosen a text that stresses applications. The program is primarily designed as an adventure in applied mathematics and many examples will be drawn from physics or engineering, but we will definitely examine both the historical and philosophical foundations of mathematics as well as using mathematically rigorous proofs in some portions of the program. The catalog states that credit will be awarded in number theory and functional analysis, but that is not correct. Upper division credits for the program are dependent on performance at an upper division level. (Upper division performance includes being present at virtually all classes, turning in all homework on time with substantial writing, doing well on exams, giving good presentations, etc. NO UPPER DIVISION CREDIT WILL BE AWARDED TO ANYONE LEAVING THE PROGRAM BEFORE THE END OF SPRING QUARTER. Differential Equations, Linear Algebra, and an Introduction to Mathematica are lower division at all colleges, but I can justify upper division credit for fall and winter quarters based on the advanced level of understanding of such topics that occur for those who continue to study them throughout the year.

What can I do to prepare?

1. Prerequisites: two quarters of calculus. Three quarters would be better.
2. Most important: Come ready to start! Have your living situation settled before classes start, so you're ready to start learning seriously in the first week. Have a functional study area, reliable transportation, and money for books. The books will costs over $500 and must be purchased by the second day of class. Be prepared to work about 50 hours per week (including class time) starting the first day of class. Students working at a job more than 12 hours per week outside of class tend to have difficulty with the workload. We are scheduled to meet from 1 p.m. to 6:30 p.m. Tuesday, Thursday, and Friday. Tutors will probably be available on Monday afternoon and on Wednesday afternoon, so keep those times free, too.

Frequently Asked Questions

• Which books do I need for the first class? Just the differential equations books by Blanchard. Read Section 1.1 before the first class. However, all the books need to be purchased by the second class, so come with the money to buy books. DO NOT COUNT ON YOUR FINANCIAL AID TO BE READY FOR YOU! Experience has shown that students who are unable to buy books during the first week have a very difficult time catching up and usually end up dropping out of advanced mathematics and science programs. Come with the money ($570) to buy your texts immediately after the first class!
• Can I drop the seminar portion of the program? No. Seminar is a tool for learning not a separate portion of the class. We will use two hours each week for class discussions of philosophical, historical, and scientific issues.
• Can I take portions of the program? Not in fall quarter unless you already have credits in an identical mathematics class (differential equations or linear algebra).
• What proportion of the credits are upper division? It is possible to earn 48 upper division credits in this program depending on performance. At any other college, linear algebra and differential equations are not considered upper division work, so upper division credit depends on exceptionally high-level performance in these areas and the depth which comes from continuing your study of these topics through spring quarter.
• Are we required to subscribe to journals? Yes. You'll get more information on the first day of class. The Mathematical Association of America has a nice deal for students - $30 for 2 journals. These will help us become part of the community of mathematicians, follow the "hot" news, and learn some nifty mathematics.
• Will I have the equivalent of a mathematics degree at the end of this year? No, but you'll have a excellent start on one! You will also have most of the prerequisites for further work in physics and engineering. More information on first day of class. See the next two questions.
• Will I fulfill the requirements for an endorsement for teaching high school mathematics by taking this program? You will fulfill some but not all of the requirements for your endorsement. Bring the checklist to go over it with me.
• What other mathematics beyond the first year level is available at Evergreen? This is the main mathematics program beyond the calculus level that is offered this year. There will be a bit of discrete mathematics in the Data to Information program this year. Next year, the Mathematical Systems program will offer additional upper division mathematics. The Mathematical Methods program is designed to be a more applied approach than the more proof-based approach of Mathematical Systems. However, the Mathematical Methods program will involve proofs as well, but the emphasis is on learning to use the mathematics of differential equations, linear algebra, etc.
• Is Mathematical Methods the right program for me or should I be in Matter and Motion? Matter and Motion covers first year calculus and calculus-based physics. Mathematical Methods requires calculus as prerequisite.
• Will it be fun? You bet! Will it be a lot of work? Yes, about 50 hours per week including in-class time.
• Are the syllabi for the year ready? Yes. through the Evergreen web site under fall quarter programs. I will also post them on my office door (room 2002, Lab I), and the door of our classroom – room 2242, Lab II. If you are new to the campus, you might want to find the classroom before the first day since we’ll cover important information about the year in the first hour of the first class.
• First meeting: Tuesday, October 1 at 1 p.m in room 2242 of Lab II

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SYLLABI FOR YEAR FOLLOW – these are all subject to revision

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Mathematical Methods 2002-2003 Differential Equations Syllabus

Tuesdays 1 – 6:30 p.m. Room 2242, Lab II Draft of August 14, 2002

Texts: Differential Equations, SECOND edition by Blanchard, Devaney, Hall - bring to every class; get correct edition!

AEM = Advanced Engineering Mathematics by Kreyszig

Link to DiffEq SYLLABUS

Tutor day and time: Monday 1 – 5 p.m. Lab II room 2211 (down the hall from our classroom)

Mathematical Methods 2002-2003 Student Presentations Syllabus

Draft of August 11, 2002

GOALS: 1. Practice communicating mathematical ideas using words, blackboard, and overhead projector.

Do at least 2 examples in your presentation. You might want to read the material in an introductory calculus book, too.

You’ll have 20 minutes for your presentation + 5 minutes for questions. We’ll use 5 more minutes for feedback.

All 3 presenters for a given day should practice their presentations with each other at least one day before your presentation to the class. If one of your co-presenters is absent, the two (or one) remaining should be prepared to cover all of the material for that day. For your 1^st presentation: Use the blackboard only; have 1-page handout with big TITLE at top, plus name & date.

For your 2^nd presentation: Use the overhead projector; have 1-page handout with big TITLE at top, plus your name & the date.
 

Wk	Date	Day	Section	Topics: Multivariable (Vector) Calculus – Chapters 8 & 9 Complex Analysis – Chapters 12 – 14	Presenter
1	Oct. 4	Friday	8.1, JRA 2.1-2.2	Vector Algebra in 2-space (the plane)  Vector Algebra in 3-space	Tutor Tutor
2	10	Thursday	8.2 8.3 JRA 2.3	Inner (Dot) Product  Vector (Cross) Product Geometric Properties of Cross Product and Triple Products
2	11	Friday	8.4 App. 3.2 8.4	Vector and Scalar Functions and Fields. Partial Derivatives Vector Calculus
3	17	Thursday	8.5 8.5 8.6	Curves. Tangents. (1st Introduction to Differential Geometry) Arc Length. Parameterization  Curves in Mechanics. Velocity and Acceleration
3	18	Friday	JRA 2.4 8.8 8.8	Lines and Planes in Space Chain Rule for multivariable (also cover single variable 1st) Mean Value Theorem (use old calc. text to go over single variable, 1st)
4	24	Thursday	8.9 8.10 8.10	Gradient of a Scalar Field. Directional Derivative Divergence of a Vector Field Divergence
4	25	Friday	8.11 8.11 A74 - 76	Curl  Curl Kronecker Delta and Curl proofs EVERYONE STUDY pp. 461 - 463
5	31	Thursday	9.1 9.2 9.3	Line INTEGRALS Line Integrals Independent of Path Double Integrals
6	Nov. 7	Thursday	9.4 9.5 9.6	Green’s Theorem Surfaces: Parameterization, Tangents, Normals Surface Integrals
7	14	Thursday	9.7 9.8 9.9	Divergence Theorem Applications of Divergence Theorem Stokes’s Theorem EVERYONE STUDY p. 523
8	21	Thursday	12.1 12.2 12.3	Complex Numbers. Complex Plane Polar Form of Complex Numbers. Powers and Roots. Derivative. Analytic Function
9	Dec. 5	Thursday	12.4 12.5 12.6	Cauchy-Riemann Equations. Laplace’s Equation. (Challenging) Geometry of Analytic Functions: Conformal Mapping (Challenging) Exponential Functions (Challenging)
10	12	Thursday	13.1 13.2 13.3	Line Integral in the Complex Plane (Challenging)  Cauchy’s Integral Theorem (Challenging) Cauchy’s integral Formula (Challenging)
1	Jan. 9	ALL on Thursday	13.4 14.1 14.2	Derivatives of Analytic Functions (Challenging) Sequences, Series, Convergence Tests Power Series
2	16		14.3	Depends on number of students. ..
3	23	YOUR CHOICE OF TOPICS for winter and spring! Three additional presentations plus your final presentation on your spring project. I urge you to consider Chapter 5 – 7 in our Linear Algebra text (Applications of Eigenvalues or Vector Spaces) and Chapter 8 (Discrete Dynamical Systems) in our Differential Eq. text.

Mathematical Methods 2002-2003 LINEAR ALGEBRA Syllabus

Fridays 1 – 6:30 p.m. Room 2242, Lab II

Draft of August 11, 2002

Texts: Introduction to Linear Algebra, FIFTH edition by Johnson, Riess, Arnold - bring to every class

Bring the current MAA journals to every class. Order those required before October 3^rd. (See notes at first day of class.)

Kreyszig’s Advanced Engineering Mathematics might be useful during fall quarter (Chapters 6 & 7), it’s required winter quarter
 

Wk	Friday Date	Read Before Class	Homework Due the following week at start of class	MAA journal
1	Oct. 4	1.1 Introduction to Matrices; Systems of Linear Eqns 1.2 Echelon Form and Gauss-Jordan Elimination 1.3 Consistent Systems of Linear Equations Order MAA journals (maa.org) BEFORE class today		Intros
2	11	1.4 Applications 1.5 Matrix Operations 1.6 Algebraic Properties of Matrix Operations		Intros
3	18	1.7 Linear Independence and Nonsingular Matrices 1.8 Data Fitting, Numerical Integration & Different’n 1.9 Matrix Inverses and Their Properties		Lib or 1059
4	25	3.1 Vector Space in Rn 3.2 Vector Space Properties of Rn 3.3 Examples of Subspaces
5	Nov 1	3.3 Examples of Subspaces 3.4 Bases of Subspaces 3.5 Dimension		CMJ 385-400
6	8	3.5 Dimension 3.6 Orthogonal Bases for Subspaces 3.7 Linear Transformations from Rn to Rm		TBA FROM CMJ
7	15	3.8 Least-Squares Solutions to Inconsistent System 3.9 Theory and Practice of Least Squares 4.1 EIGENVALUE PROBLEMS
8	22	4.2 Determinants and the Eigenvalue Problem 4.3 Elementary Operations and Determinants 4.4 Eigenvalues and the Characteristic Polynomial
9	Dec 6	4.5 EIGENVECTORS AND EIGENSPACES 4.6 Complex Eigenvalues and Eigenvectors 4.7 Similarity Transformations and Diagonalization
10	13	4.7 Diagonalization 4.8 Difference Equations: Systems of Diff. Eqn’s.
	20	Evaluation Conferences: stay through December 20th
1	Jan 10	4.8 7.1 Quadratic Forms 7.2 Systems of Differential Equations (review!?)
2	17	7.3 Transformations to Hessenberg Form 7.4 Eigenvalues of Hessenberg Matrices 7.5 Householder Transformations
3	24	7.6 The QR Factorization and Least-Squares Sol’ns 7.7 Matrix Polynomials & the Cayley-Hamilton Thm 7.8 EV’s and Solutions of Systems of Diff. Eq’ns
4	31	Numerical Linear Analysis Kreyszig 18.6 – 18.9;
5	Feb 7	Exam part 1; class will meet
6	14	EXAM & Review. ( faculty retreat, but class will meet)
7	21	See Differential Geometry Syllabus for rest of quarter
8	28	DG
9	Mar 7	DG
10	14	DG
1	Apr 4	CALCULUS OF VARIATIONS (see DG syllabus)

c:\math methods\SYLLABUS Lin Alg YEAR

Tutor: Wednesday 1 – 5 p.m. Lab II room 2211 (just down the hall from our classroom)

Mathematical Methods 2002-2003 Differential Geometry Syllabus

Draft of August 11, 2002

Winter: Thursdays 1 – 6:30 p.m. plus Fridays during winter quarter weeks 7 through 10

Spring: Fridays 1 – 6:30 p.m. plus Thursday of 1^st week of spring quarter

Text: Differential Geometry and Its Applications by John Oprea

Recommended or required: Schaum’s Outline - Differential Geometry; Grya’s Modern Diff’l Surfaces
 

Wk	Date	Read Before Class (from Oprea’s text)		Homework Due the following week	AEM	Pres’n or journal
1	Jan 9 Th	1 The Geometry of Curves			8.5	CMJ
2	16 Th	1			8.7	AMM
3	23 Th	2 Surfaces			9.5
4	30 Th	2			9.6
5	Feb 6 Th	3 Curvature			8.7
6	13 Th	Class will meet. Don at Faculty Retreat?
7	20 Th	3 Curvatures
7	21 Fri	4 Minimal Surfaces
8	27 Th	4 Constant Mean Curvature Surfaces; Harmonic functions
8	28 Th	5 Geodesics, METRICS
9	Mar 6 Th	5 Isometries and Conformal Maps			12.5
9	7 Fri	6 Covariant Derivative & Parallel Vector Fields (and see Chapter 9 in May)
10	13 Th	6 Gauss-Bonnet Theorem
10	14 Fri	7 Complex Variables; Enneper Representations			12 & 13
1	Apr 3 Th	7 Bjorling’s Problem & Minimal Surfaces
1	4 Fri	8 CALCULUS OF VARIATIONS
2	10 Th	Rest of Thursdays reserved for spring projects		No class, but be available to meet
2	11 Fri	8 CALCULUS OF VARIATIONS
3	18 Fri	8 CALCULUS OF VARIATIONS
4	25 Fri	8 Calculus of Variations 9 Manifolds
5	May 2 Fri	9 Covariant Derivative
6	9 Fri	9 Christoffel Symbols (if time: Dual, wedge products, Killing vectors, Schwarzschild sol’n in GR)
7	16 Fri	Exam – plus take home due
8	23 Fri	No class – prepare for your final project presentation
9	30 Fri	Project Presentations – attendance required even if you’re not usually in class on Fridays
10	Jun 6 Fri	Project Presentations
EVALUATIONS START JUNE 19TH – DON’T LEAVE BEFORE JUNE 20TH ! No conference w/o faculty evaluation

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