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Linear Algebra And Its Applications
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Math 215

Linear Algebra

General Information

Schedule

Homework

Books and Online Resources

We will not follow an official textbook. Instead, I will write course notes that I will post here: Current Notes.

For an excellent overview of the core ideas of Linear Algebra (with high quality visualizations), I strongly recommend the video series Essence of Linear Algebra by 3Blue1Brown.

In addition, I encourage you to consult other books and online resources to help learn the material, as these sources provide different perspectives on the subject. For linear algebra books, I recommend the following:

Linear Algebra by Jim Hefferon. Available online.
A Course in Linear Algebra by David B. Damiano and John B. Little.

We will also spend a significant portion of time learning how to write mathematical proofs. For additional references on mathematical writing and notation, I recommend the following:

Book of Proof by Richard Hammack. Available online.
Mathematical Reasoning: Writing and Proof by Ted Sundstrom. Available online.
How to Prove It by Daniel Velleman.

For general advice on making the transition from a computational perspective of mathematics to a more conceptual understanding (including how to think logically and how to write mathematics), consider reading the following:

How to Think Like a Mathematician by Kevin Houston.
How to Study as a Mathematics Major by Lara Alcock.

Administrative Information

Instructor	Joe Mileti
Office	Noyce 2514
Office Hours	Monday 9:30 - 10:30 Tuesday 3:15 - 4:30 Wednesday 1:30 - 2:30 Thursday 9:00 - 10:30 Also By Appointment
Email	miletijo ~at~ grinnell ~dot~ edu
Phone	641-269-4994
Class Time	MWF 3:00 - 3:50
Classroom	Noyce 2243

Course Mentors	Yuki Takahashi
Mentor Session Room	Noyce 2243
Mentor Session Times	Tuesday 5:00 - 6:00 Thursday 4:00 - 5:00 Sunday 5:00 - 6:00

A Course In Linear Algebra Damiano Ebookers Free

Course Objectives

Develop the ability to apply conceptual ideas in order to solve problems, and appreciate the importance of how the relevant theoretical ideas can simplify (or allow one to completely avoid) complex computations.
Learn how to interpret and use mathematical language properly, with an emphasis on quantifiers (there exists, for all), connectives (and, or, not, implies), and the role of definitions.
Learn how to interpret and use common mathematical notation involving sets and functions.
Learn how to read mathematical exposition with the goal of understanding, rather than with the aim of solving a narrow class of rigid problems.
Understand the logic of mathematical arguments, different ways to prove a statement, and how to construct your own proofs.
Learn some of the fundamental concepts of linear algebra: spans, linear transformations, matrices, solving linear systems, vector spaces, subspaces, dimension, linear independence, determinants, and eigenvalues/eigenvectors.
Develop an appreciation for the power and elegance of mathematical structures (such as vector spaces).

Homework

There will be two different types of homework assignments:

Problem Sets will be due on most Mondays and Fridays. They contain a mixture of computational exercises, explanations, and short proofs.
Writing Assignments will be due on most Wednesdays, and will also be posted to the course webpage. These problems are more conceptual or theoretical, and will require significant explanation. Your solutions should consist of careful arguments written in complete sentences (augmented by mathematical symbolism where appropriate). A major goal of these problems is to teach the fundamentals of mathematical language and mathematical inferences, along with proper use of terminology and notation. As a result, they will be graded at a high standard involving much more than getting the 'correct answer'. Take the time to write and revise these as you would in a paper in other courses.

Policies for all homework assignments:

Homework assignments and solutions will be posted to the course webpage.
Please take the time to write your solutions neatly and carefully! All homework assignments consisting of more than one page must be stapled.
Homework is due at the beginning of class (i.e. at 3:00pm). If you are late for class, but turn an assignment in when you enter, your homework will be subject to a 10% penalty. Unless you have a serious emergency that you bring to my attention before a homework assignment is due, assignments turned in after class will not be accepted for credit.
Your lowest two Problem Set scores and your lowest Writing Assignment score will be dropped.

If you want to learn how to present your work professionally, as well as keep digital records, I recommend learning how to type your solutions. LaTeX is a wonderful free typesetting system which produces high-quality documents at the cost of only a small amount of additional effort (beyon