MAT 326 Introduction to Linear Algebra

"Cogito ergo sum" ("I think, therefore I am")
René Descartes, 1596-1650

  • Textbook

    • Introduction to Linear Algebra, Second Edition, Serge Lang, Springer, 1986.

  • Topics

    • Vectors, Matrices and Linear Equations, Vector Spaces, Linear Mappings, Composition and Inverse Mappings, Scalar Products and Orthogonality, Determinants, Eigenvectors and Eigenvalues

  • Class Meeting Times and Class Room

    • Monday/Wednesday 3:30-4:45pm in Southern Hall 303

  • Office Hours

    • Monday/Wednesday 2:00-3:30pm and by appointment

  • Grading

    • 3 In-Class Exams (90%) and Homework (10%). Final Exam is optional and if taken, its grade will replace the lowest exam grade.

    You can view your raw grade here. You can view your processed grade including the final grade for the course here. You can identify yours by the last four digits of your student id.

  • Math Forum

    • If you have a question, you may post a question on my Math Forum site. This forum site is equipped with MathJax which supports LaTex, a wonderful type setting system that is really good at formatting mathematical formulas and equations. MathJax allows us to write mathematical formulas and equations in popular web platforms using LaTex code.To include LaTex code in your posts and comments, use:

    \open parenthesis your-LaTex-code-here\close parenthesis

    You can find a list of Latex codes for math symbols here. You may practice your Latexing here. Here is another site where you can practice Latex but you don't put \open parenthesis and \close parenthesis there, only codes.

    If you want to try Latex in your Windows computer, you may download it for free from MikTex Project Page. If you are using a Linux distribution, usually Latex is a part of the standard packages repository. (The package is called texlive.) To use Latex, you need an editor. Texmaker is a nice interface for using Latex. You can edit/compile/view all together in Texmaker. If you don't want to deal with commands, there is a WYSWYG (What You See is What You Get) interface for Latex called Lyx.

  • Sage and Linear Algebra

    • Sage is an open source math software whose interface is a web browser (in particular firefox). You don’t have to install Sage in your computer to use it. You can access any sage server including the main Sage server. I am running a Sage server at sage.st.usm.edu. Any student at the University of Southern Mississippi is more than welcome to create an account at sage.st.usm.edu and use it.

    Click on the following links to learn how to use Sage in studying Linear Algebra:

    Sage Quick Reference: Linear Algebra by Robert A. Beezer

  • Weekly Schedule

    • Week
    Date
    Sections
    Homework
    Notes
    1
    8/21
    		 1.1 Definition of Points in Space, 1.2 Located Vectors p8/all, p12/all
    2
    8/26
    		 1.3 Scalar Product, 1.4 The Norm of a Vector, 1.5 Parametric Lines, 1.6 Planes p15/all, p29/all but #9, p34/all, p40/all
    3
    9/2
    		 2.1 Matrices, 2.2 Multiplication of Matrices, 2.3 Homogeneous Linear Equations and Eliminations (reading) p46/all, p58/3,5,7,9,13,16-21 No class on 9/2 Labor Day Holiday.
    Turn in homework p15/5 and p29/7 by Wed 9/4.
    4
    9/9
    		 2.4 Row Operations and Gauss Eliminations, 2.5 Row Operations and Elementary Matrices, 2.6 Linear Combination p76/1,2,3,4, p85/1 Turn in homework p40/2 by Wed 9/11.
    5
    9/16
    		 3.1 Definitions, 3.2 Linear Combinations, 3.3 Convex Sets (reading) p93/all Turn in homework p46/5,6,10 by 9/16. Turn in homework p58/21 (c), (d), (e) by 9/18.
    6
    9/23
    		 3.4 Linear Independence p109/1-7,11 Exam 1 (Chapters I and II) on Wednesday 9/25
    7
    9/30
    		 3.5 Dimension, 3.6 The Rank of a Matrix, 4.1 Mappings (reading) p121/1, 2 Wednesday 10/2: Last day to drop without academic penalty.
    8
    10/7
    		 4.2 Linear Mappings, 4.3 The Kernel and Image of a Linear Map, 4.4 The Rank and Linear Equations Again (reading) p134/1,5,6,10, p141/1,3,4,6,7,8,9 Turn in homework p93/1,5 by Wednesday 10/9.
    9
    10/14
    		 4.5 The Matrix Associated with a Linear Map, 5.1 Composition of Linear Maps p156/1,2,3,4,6,7,8, p162/1,6,7,8 10/17-10/18 Fall Break
    10
    10/21
    		 5.2 Inverses, 6.1 Scalar Products p169/1,3,4,5,6,7,8,9,11,13, p178/1,2,3,4,8,9,10,11,12,13
    11
    10/28
    		 6.2 Orthogonal Bases, 6.3 Bilinaer Maps and Matrices (skipped), 7.1 Determinants of Order 2 p189/1-8 Exam 2 (Takehome) (Chapters III, IV and V) will be given on Wednesday 10/30 at 3:30pm (It is due by 3:30pm on Monday 11/4. Absolutely no late submission!)
    12
    11/4
    		 7.2 \(3\times 3\) and \(n\times n\) Determinants, 7.3 The Rank of a Matrix and Subdeterminants, 7.4 Cramer's Rule p207/1,2,3,4,6, p214/1-8, p217/1
    13
    11/11
    		 7.5 Inverse of a Matrix, 7.6 Determinants as Area and Volume, 8.1 Eigenvectors and Eigenvalues p221/1, p232/2,3,4, 237/all Turn in homework p178/1,2 by Wednesday 11/13.
    14
    11/18
    		 8.2 The Characteristic Polynomial, 8.3 Eigenvalues and Eigenvectors of Symmetric Matrices p249/all (12, 13 are for students who already have taken Calculus I), p255/all (optional)
    15
    11/25
    		 8.4 Diagonalization of a Symmetric Linear Map p259/all (optional)
    THANKSGIVING HOLIDAYS 11/27-11/29
    16
    		 12/2 Review Exam 3 Chapters VI, VII and VIII on Wednesday 12/4 For the exam make sure that you study at least those topics listed in the study guide.
    Turn in sage homework by 10:00pm on Friday 12/6. This is optional and for those who wish to receive extra points for Exam 2.
    17
    12/9
    FINAL EXAM WEEK
    		 Final Exam on Monday 12/9 4:15pm-6:45pm