Teaching

Some new material were posted on Friday, November 13, 2009

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PROBLEM OF THE MONTH - NOVEMBER

Problem 1
Problem 2

COURSE SYLLABI MATH 200
Syllabus

MATH 165
Syllabus

MATH 162 (MWF)
Syllabus

MATH 162 (TTh)
Syllabus

QUIZZES/HOMEWORKS

MATH 201
Math 201 (List of Homework Problems Fall 2008)

MATH 200
Math 200 (List of Homework Problems Fall 2009)

MATH 165
Math 165 (List of Homwework Problems for Fall 2009)

MATH 162
Math 162 (List of Homework Problems Fall 2009)(NEW !- Updated 11/13//09)

AUXILIARY MATERIAL FOR COURSES

MATH 370

Here are some sample chapters (Chapters 2-5) from the Abstract Algebra book by Charles Pinter. However, due to the copy rights, I am unable to put more chapters. The ordering information is available from the instructor.

1. Chapter 2 (Operations)
2. Chapter 3 (Definition of Groups)
3. Chapter 4 (Elementary Properties of Groups)
4. Chapter 5 (Subgroups)

COPIES OF TRANSPARENCIES

1. Group Definition
2. Examples and Non-Examples of Groups
3. Power Set of a Given Set
4. The Principle of Mathematical Induction (Basic Version)
5. How to use Mathematical Induction to do two problems in Group Theory (related to commuting elements)
6. Two related problems on subgroups
7. Given that H and K are two subgroups of G. Prove that the intersecton of H and K is a subgroup, and also to prove that HK is a subgroup provided that G is abelian
8. The center Z(G) of given group G
9. The centralizer of an element in a group G
10. A certain subgroup of the direct produt group G X H
11. G is any abelian group, and H is any subgoup of G. Let K be the elements of G whose squares are in H. Then prove that K is a subgoup of G
12. The homomorphic image of any subgroup is also a subgroup (C3, page 143)
13. The center of any group is a normal subgroup of that group (D3, page 143)
14. The intersection of any two normal subgroups is also a normal subgroup ( A special case of D6, page 143)

SPECIAL NOTE:At this point, I have done most of your homework problems, i.e. E1, pg 99 (in class), E3, pg 99 (in class), G1, pg 100 (in class), B3, pg 142 (in class), C2, pg 143 (in class), C3, pg 143 (home page), D2, pg 143 (in class), D3, pg 143 (home page), D6, pg 143 (home page). This is a total of 9 problems, and consists of most of the assigned problems on the Chapters 9 and 14. Please study very hard for the test and I will be available on Monday to answer some more. Some of the key words that you can study, but NOT LIMITED TO, are, injection, surjection, bijection, permutation, Symmetric Group, Group of Symmetries, group homomorphism, monomorphism, epimorphism, isomorphism, automorphism, endomorphism, kernel of a homomorphism, normal subgroup, center of a subgroup, etc. The test will cover the material taught through last Tuesday (April 4), and Thursday (April 7) I gave a good review. GOOD LUCK TO EACH ONE OF YOU ON THE TEST!

MATH 312

COPIES OF TRANSPARENCIES

0. Go to Math 162 (Trigonometry), Math 200, and Math 201 sections below, and print the necessary transparencies. They will be quite helpful to polish up your trigonometry, and differentiation & integration formulas. Memorize them!
1. Definitions of Vector Operations
2. Properties of Vector Operations
3. How to Normalize a Vector (CRUCIAL)
4. Visulaizing the Eight Octants (and the room with the best view!!)
5. Properties of the Dot Product
6. The Connection Between the Dot Product and the Angle Between the Two Vectors
7. The Famous Triangular Inequality and its Proof
8. Cauchy-Schwarz Inequality and its Proof
9. THE PROJECTION OF A GIVEN VECTOR ONTO ANOTHER VECTOR
10. The Cross Product of Two Vectors - Definition
11. The Cross Product of Two Vectors - Algebraic and Geometric Properties
12. The Equation of a line in Space - Parametric and Symmetric Forms
13. The Equation of a Plane in Space
14. Calculaitng the Distance from a Point to a Plane - An example
15. Calculating the Distance from a Point to a Plane - The General Formula and its Proof
16. Gradient, Divergence, and Curl (Definitions)
17. Gradient, Divergence, and Curl (Examples- page 1)
18. Gradient, Divergence, and Curl (Examples - page 2)
19. Answers to some questions: Gradient, Divergence, and Curl
20. Gradient, Divergence, and Curl (Vector Identities)
21. Answers to SomeVector Identities