**As Taught in**:

2018/2019

**Level**:

Undergraduate

**Learning Resource Types:**

=> Problem Sets

=> Notes from instructor insights

=>Reading Resources

**Course Description:**

Linear Algebra of Communication is a supplement to “Introduction to Linear Algebra”. The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic – abstract root systems in an Euclidean Space.

**Course Overview:**

Linear Algebra of Communication is a communication supplement to “Introduction to Linear Algebra”. We will go over the “Introduction to Linear Algebra” Syllabus, considering some topics in more depth. The main emphasis will be on the methods of creating rigorous and elegant proofs and presenting them clearly in writing.

**Course Meeting:**

Lectures : 1 session for 1 hour / week

**Course Format:**

Linear Algebra of Communication will meet once a week for an hour, and additionally for 30 minutes in smaller groups. We hope to have at least one class in a computer lab working with the publishing program LaTeX.

**Prerequisites:**

Introduction to Linear Algebra

**Recommended Text**:

There is no required text, but if learner have the book normally used as a textbook for “Introduction to Linear Algebra”, it might be helpful.

Strang, Gilbert. 2009, February. *Introduction to Linear Algebra 4th Ed*. Published by Wellesley-Cambridge Press. ISBN: 9780980232714.

**Practices**

There will be a weekly written projects and a final project, which should be about five printed pages long. Time allowing, each learner will make a presentation in class on the subject of their final paper. There is no solving question final exam.

**Note**:

To succeed in this course learner will need to be comfortable with vectors, matrices, and three-dimensional coordinate systems. Linear Algebra material is presented in the first few lectures of *Calculus-102*, and again in here.

The basic operations of Linear Algebra are those learner learned in grade school – addition and multiplication to produce “Linear Combinations.” But with vectors, we move into four-dimensional space and n-dimensional space.

**A topic that will be covered are:**

- Introduction to Mathematical Writing
- Linear Spaces
- Basis and Dimension
- Linear Mappings
- Matrices
- Publishing Program LaTeX
- Subspaces and Direct Sums
- Reflections in a Euclidean Space
- Abstract Root Systems
- Simple and Positive Roots
- Properties of Simple Roots
- Cartan Matrix of a Root System
- Dynkin Diagrams and Classification

Resource gives users access to most of the course resources in a single location. (Please get your education login and access to each of them).

*The Not so Short Introduction to***LaTeX***Essential***LaTeX**++*Using Imported Graphics in***LaTeX**

The material below will help you learn and use LaTeX, as well as prepare for giving presentations during the course.

Sample .tex files: (please log in to access it):

- sample 1 .tex
- sample 2 .tex
- sample 3 .tex
- sample 4 .tex
- sample 5 .tex
- matr1 .tex

Below are the project in three formats (.tex and .pdf). Sample learner projects are included courtesy of the learners listed. The projects are due during the week noted in the topics.

Week 8 : Project 1 – Reflections in a Euclidean Space (please log in to download, upload, and check sample files)

Week 9 : Project 2 – Abstract Root Systems (please log in to download, upload, and check sample files)

Week 10 : Project 3 – Simple and Positive Roots (please log in to download, upload, and check sample files)

Week 12 : Project 4 – Properties of Simple Roots (please log in to download, upload, and check sample files)

Week 13 : Project 5 – Cartan Matrix of a Root System (please log in to download, upload, and check sample files)

Week 14 : Project 6 – Dynkin Diagrams and Classification (please log in to download, upload, and check sample files)