This course page is obsolete.  I'll prepare a new page next time I teach the course.

General information

• General description. Math 130 is a requirement for mathematics and physics majors, and it's highly recommended for majors in other sciences especially including computer-science majors. Topics include systems of linear equations and their solutions, matrices and matrix algebra, inverse matrices; determinants and permutations; real n-dimensional vector spaces, abstract vector spaces and their axioms, linear transformations; inner products (dot products), orthogonality, cross products, and their geometric applications; subspaces, linear independence, bases for vector spaces, dimension, matrix rank; eigenvectors, eigenvalues, matrix diagonalization. Some applications of linear algebra will be discussed, such as computer graphics, Kirchoff's laws, linear regression (least squares), Fourier series, or differential equations.
  See also Clark's Academic Catalog.
• Prerequisites. The prerequisite for the course is one year of college calculus, others by permission only.
• Course goals.
  • To provide students with a good understanding of the concepts and methods of linear algebra, described in detail in the syllabus.
  • To help the students develop the ability to solve problems using linear algebra.
  • To connect linear algebra to other fields both within and without mathematics.
  • To develop abstract and critical reasoning by studying logical proofs and the axiomatic method as applied to linear algebra.
• Syllabus.
• Course objectives. Students will be able to apply the concepts and methods described in the syllabus, they will be able to solve problems using linear algebra, they will know a number of applications of linear algebra, and they will be able to follow complex logical arguments and develop modest logical arguments. The text and class discussion will introduce the concepts, methods, applications, and logical arguments; students will practice them and solve problems on daily assignments, and they will be tested on quizzes, midterms, and the final.
• Textbook. The text for the course is Introductory Linear Algebra, an Applied First Course, 8th edition, Bernard Kolman and David R. Hill. Prentice-Hall, 2005. ISBN: 0-13-143740-2. Prentice Hall's Companion Website for the book.
• Course Hours. MWF 11:00-11:50. BP 326.
• Office hours.
• Course Schedule
• Assignments & tests. There will be numerous short assignments, mostly from the text, occasional quizzes, two tests during the semester, and a two-hour final exam during finals week in December. The two tests during the semester are yet to be scheduled.
• Course grade. The course grade will be determined as follows: 2/9 assignments and quizzes, 2/9 each of the two midterms, and 1/3 for the final exam.

Class notes, quizzes, tests, homework assignments

1. Monday, Aug 28. Notes: Welcome.
   Topic: simultaneous systems of linear equations.
   The Chinese method of elimination.
2. Wednesday, Aug 30. Notes.
   Linear systems. Introduction to matrices.
   Assignment due: exercises from section 1.1: 1-4, 13-14, 21-22, 23, and T4.
3. Friday, Sep 1. Notes.
   Vectors and their dot products, matrix multiplication, summation notation.
   Assignment due: exercises from section 1.2: 1-2, 4-7 parts a-d each, 8, 9, T1, T5a.
4. Wednesday, Sep 6. Notes.
   Properties of the matrix operations, powers of matrices, symmetric matrices.
   Assignment due: exercises from section 1.3: 1-4, 7, 9, 11-12, 19-20, 33, T1, T4.
5. Friday, Sep 8. Notes.
   Quiz 1, covering through section 1.3. Answers
   Matrix transformations from Rⁿ to R^m
6. Monday, Sep 11. Notes.
   Analysis of the method of elimination, elementary row operations, homogeneous systems.
   Assignment due: exercises from section 1.4: 11-13, 19, T.10, T.24, and T.30.
   Determine date of first test.
7. Wednesday, Sep 13. Notes.
   Elementary row operations and associated elementary matrices, homogeneous systems, introduce inverse matrices.
8. Friday, Sep 15. Notes.
   Properties of inverse matrices, a general method to find inverse matrices.
   Assignment due: exercises from section 1.5: 1-2, 5-6, 15-17.
9. Monday, Sep 18. Notes.
   Introduction to determinants, permutations and their parity.
   Assignment due: exercises from section 1.6: 1-8, 13-14, 20, 28, T8.
10. Wednesday, Sep 20. Notes.
    Definition of determinants and a few of their properties
    Assignment due: exercises from section 1.7: 1-4, 9, 11, 12, 17a, 22, T4, T5.
11. Friday, Sep 22. Notes.
    Properties of determinants and an efficient way to compute them.
    Assignment due: exercises from section 3.1: parts a and b only of 1-6, 15, 19, and 20.
12. Monday, Sep 25. Review.
13. Wednesday, Sep 27. First midterm. Answers.
14. Friday, Sep 29. Kirchhoff's laws.
    Dave's Square Dissection Puzzles.
15. Monday, Oct 2. Notes.
    Cofactor expansion.
16. Wednesday, Oct 4. Notes.
    Cramer's rule, vectors in the plane, dot product, length.
    Assignment due: exercises from section 3.1: T1, T6, and T12.
    See Dave's short course on trig for a general review of trigonometry
17. Friday, Oct 6. Notes.
    Law of cosines, orthogonal vectors, areas of triangles and parallelograms, standard unit vectors, vectors in dimension n, vector operations
    Assignment due: exercises from section 3.2: 1, 3ab, 4ab, 10ab, 11ab, 20, 23.
18. Wednesday, Oct 11. Notes. Length of a vector, dot products, and angles in n-space, the triangle and Cauchy inequalities.
    Assignment due: exercises from section 4.1: 3, 5, 9ab, 13, 19, 21ab, 22ab.
19. Friday, Oct 13. Notes. More on the Cauchy inequality, unit vectors in n-space, and linear transformations. L : Rⁿ->R^m.
    Assignment due: exercises from section 4.1: 23, 24, 27, 28, T5, T7.
20. Monday, Oct 16. Notes. Cross Products in R³ and their properties.
    Assignment due: exercises from section 4.2: 8, 10ab, 11ab, 12ab, 14, 21ab, 23.
21. Wednesday, Oct 18. Notes. More on cross products.
    Assignment due: exercises from section 4.2: 25, 26, 27ab, 31, 32, 34, T7, T10.
22. Friday, Oct 20. Notes. Lines and planes in R³.
    Assignment due: exercises from section 4.3: 1, 4-7, 21, 22.
23. Monday, Oct 23. Notes. Introduce abstract vector spaces.
    Assignment due: exercises from section 4.3: 25, 26, 27, 29, T9, T10, T11.
24. Wednesday, Oct 25. Notes. Properties of vector spaces.
    Assignment due: exercises from section 5.1: 1ab, 2ab, 9-12, T2, T3, T4, T5.
25. Friday, Oct 27. Notes. Subspaces.
    Assignment due: exercises from section 5.2: 5ab, 6ab, 10ab, 13, T3. Answers
26. Monday, Oct 30. Notes. Solution spaces, span of a set.
    Assignment due: exercises from section 6.1: 11, 15, 20, T3.
27. Wednesday, Nov 1. Notes. Concepts of linear independence and basis.
    Assignment due: exercises from section 6.2: 1-3, 5, 6, 9 14, 17-19.
28. Friday, Nov 3. Notes. Dimension of a vector space.
    Assignment due: exercises from section 6.2: 23-25, 27, T4, T10.
29. Monday, Nov 5. Review.
30. Wednesday, Nov 8. Second test. Section 3.2 through 6.1. Answers.
31. Friday, Nov 10. Notes. A constructive method to select linearly independent vectors from a spanning set.
32. Monday, Nov 13. Notes. The solution set of a homogeneous system of linear equations as a subspace of Rⁿ
    Assignment due: exercises from section 6.3: 1, 2, 6-10.
33. Wednesday, Nov 15. Notes. The solution set of a nonhomogeneous system of linear equations; row space, column space, row rank, column rank of a matrix.
    Assignment due: exercises from section 6.4, exercises 1, 2, 7, 9, 11, 15, 18, 20, 22, 28, 31, 35, T2.
34. Friday, Nov 17. The row rank and column rank of a matrix are equal.
    Assignment due: exercises from section 6.5, exercises 1, 3, 4, 8.
35. Monday, Nov 20. Notes. Coordinates with respect to a basis, changing between standard coordinates and coordinates with respect to another basis
    Assignment due: exercises from section 6.6, exercises 3-6, 18-22, T6, and T10.
36. Monday, Nov 27. Notes. Changing between coordinates with respect to two different bases
37. Wednesday, Nov 29. Quiz. Notes. Eigenvalues, eigenvectors, and the characteristic polynomial.
    Assignment due: exercises from section 6.7, exercises 1, 2, 7, 8, 13, 14.
38. Friday, Dec 1. Notes. Eigenvalues and eigenvectors of example transformations of the plane, the complex numbers C, and vector spaces over C. Introduction to similar matrices.
    Dave's short course on complex numbers
39. Monday, Dec 4. Notes.
    Assignment due: exercises from section 8.1, exercises 2--5, 8--10.
40. Wednesday, Dec 6. Notes.
    Assignment due: more exercises from section 8.1, exercises 16ab, 18, T3.
41. Friday, Dec 8. Discussion of 8.2.
42. Monday, Dec 11. Review.
43. Monday, Dec 18. Final Exam. Answers.

Last year's midterms and final

• First midterm
• Second midterm
• Final examination

Pages on the web that you may find interesting

• Humor in mathematics
• MathArchives links for Linear and Matrix Algebra.
• Articles by J J O'Connor and E F Robertson on the history of Abstract linear spaces and on the history of Matrices and determinants at The MacTutor History of Mathematics archive.
• Dave Rusin's The Mathematical Atlas describes the subject of linear algebra and its subfields, at Northern Illinois University.
• On-line textbooks:
  • Linear Algebra: An Introduction to Linear Algebra for Pre-Calculus Students. by Tamara Anthony Carter, Richard A. Tapia, and Anne Papakonstantinou, at Rice University. You may find this text useful especially for the first part of our course.
  • Linear Algebra by Jim Hefferon, at Saint Michael's College. This text has many of topics in our syllabus.
  • Elementary Linear Algebra, lecture notes by Keith Matthews. This text also has many of the topics in our syllabus.
  • Linear Algebra and Applications Textbook by Thomas S. Shores. Again, many of the topics in our syllabus.

This page is located on the web at

http://aleph0.clarku.edu/~djoyce/ma130/

David E. Joyce,