Background comments: While the very beginnings of matrices and the elimination process in the context of solving systems of linear equations can be seen in Chinese writings between 200 and 100 B.C., determinants, elimination, matrices, and vector spaces were only really systematized throughout the 1800s.  Furthermore linear algebra only became a standard part of the undergraduate curriculum in the 1960s, initially as a part of other courses and then as a course in its own right.  Thus linear algebra is a relatively young field but it has rapidly become ubiquitous, both within mathematics and in many fields to which mathematics is applied.  Hermann Weyl foresaw this when he wrote in his book The Theory of Groups and Quantum Mechanics, "...the fundamental concepts of this branch of mathematics [linear algebra] crop up everywhere in mathematics and physics, and a knowledge of them should be as widely disseminated as the elements of differential calculus".  Modern computing has of course helped advance its spread, but raises important numerical issues surrounding algorithms and computations (which are primarily treated in a numerical analysis course).  

Objectives: This course will briefly touch on the rigorous framework for many of the standard manipulations with linear systems and matrices, will consider vector spaces over real or complex numbers or even more general fields, will delve more deeply into the theory of linear transformations and their standard forms, and will conclude with material on inner product spaces.

This course will help you:

• Master the theoretical framework underlying basic results of linear algebra over real or complex numbers. 
• Be able to use deeper results in linear algebra to answer computational and theoretical questions.
• Use Maple as a tool to perform tedious calculations and test conjectures.
  
• Be able to construct logical arguments to prove propositions involving the fundamental ideas and write clear proofs based on those arguments.
• Be aware of connections between linear algebra and other areas of mathematics or other fields.
  

Materials: The main text is Linear Algebra by Hoffman and Kunze.  We will most likely cover Chapters 1 and 2 very briefly in class during the first week or so and then will cover most of Chapters 3-8.  If time allows we may cover parts of Chapters 9.  You are encouraged to use the computer software package Maple as a tool to perform tedious calculations, experiment with examples, and test conjectures.  I will try to provide some guidance in its use, but I am most familiar with the older versions.  Below are listed additional references, some of which will be put on reserve at the library.

Books recommended primarily as a reference on elementary linear algebra:

• David Lay - Linear Algebra and its Applications
• Otto Brettscher - Linear Algebra with Applications
• Gilbert Strang - Linear Algebra and its Applications

Other books at a roughly comparable level as Hoffman & Kunze:

• Charles W. Curtis - Linear Algebra
• Steven Roman - Advanced Linear Algebra
• Jonathan Golan - The Linear Algebra a Beginning Graduate Student Ought to Know

• Lancaster & Tismenetsky - Theory of Matrices (for Math 633 - Matrix Theory)
• Horn & Johnson - Matrix Analysis (for Math 699 - Advanced Matrix Analysis)

Prerequisites: The official prerequisite for this course is Math 240 (the old Math 330 or a comparable introductory linear algebra course).  The ability to utilize abstract mathematical concepts and construct proofs will be important.  You will further develop these abilities in this course.

Format and Evaluation
Class time will include a mixture of brief lectures and possibly also some cooperative group work and/or computer activities in the lab, PS 324. You are responsible for material covered in all classes regardless of whether you have reason to be absent. Material covered in class lectures and activities will assume that you have read and thought about the material ahead of time.  

Those taking the course as 599 will be required to complete additional and/or more difficult problems and readings and may give an in-class presentation.

Understanding and being able to do mathematics requires consistently working on problems yourself.  But in addition to doing so you are encouraged to study together and discuss problems with others since this can be a very effective and rewarding way to learn mathematics. You must write up solutions yourself and give written credit for ideas obtained from other sources. Violations of ISU's plagiarism policy will not be tolerated and will be addressed according to ISU policy (see the Student Code of Conduct in the Student Handbook, http://www.isu.edu/studenta/handbook.pdf and the section of the Faculty Staff Handbook referenced there, http://www.isu.edu/fs-handbook/part6/6_9/6_9a.html).

Exams will likely be take-home format with strict expectations regarding independent work.  Test problems may require you to apply familiar concepts in new situations.  Brief in-class quizzes will require you to give definitions of key terms.  The exam dates and coverage listed below are tentative.  Please make note of the date of the final.

Grades of A, B, C, D will be guaranteed by earning overall percentages of 90%, 80%, 70%, 60%. Cutoffs for +/- will be within 3 percentage points of these values.  The grades and comments on individual assignments are intended to provide you with feedback and to help you assess your current state of learning.  The final course grade will reflect to what extent you have accomplished the first four goals above on what you should be able to do at the end of the course.

Philosophy: All of you have the potential to succeed in this course and hard work counts for a great deal. I continue to learn by expanding my knowledge of mathematics and its connections with other subjects, by doing original research, by understanding more about learning and teaching, and by working to teach in ever more effective ways. I expect you will deepen your knowledge of mathematics and its logical structure, will learn to formulate questions that lead you to construct your own understanding of mathematics, and will know more about the process of learning, solving problems, and writing proofs after you complete this course. The most important skill you gain during a college education is the ability to learn independently.

Accommodations: Idaho State University is committed to equal opportunity in education for all students. If you have a diagnosed disability or if you believe you have a disability that might require reasonable accommodation in this course, please contact the ADA & Disability Resource Center, Room 123 Graveley Hall (282-3599) as soon as possible.