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### TUTORIALS

The tutorials are divided into 2 separate sections. The first set of tutorials is based on general mathematical concepts. Some of these tutorials will seem familiar to students since the content is a review of algebra-related concepts from high school courses, although some of the material may be new to you. A short description of each tutorial from the General Mathematics section is listed below. To visit the tutorial, click the link below each description or the link from the menu on the left-hand side of the page.

# Notation & Methods of Proof

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> | NOTATION & METHODS OF PROOF Tutorial

# Mathematical Induction

The induction tutorial contains guidelines for proving statements using mathematical induction. This is a very powerful method of proof. The only drawback is that proof by mathematical induction can only be used for statements that have number sets that increase or decrease by integer values.

> | MATHEMATICAL INDUCTION Tutorial

# Complex Numbers

The complex numbers tutorial explains what the imaginary and real components of a complex number are. It also goes through the different ways a complex number can be written. It defines properties, conjugates, and absolute values of a complex number as well as visits some very important theorems such as DeMoivre's Theorem and Euler's Theorem.

> | COMPLEX NUMBERS Tutorial

# Polynomials

The polynomials tutorial begins with a few definitions of different terms. It also contains a section on evaluating rational expressions. The most important part of this tutorial is the section on factoring polynomial expressions. Students will be required to factor expressions in all sections of the algebra course.

> | POLYNOMIALS Tutorial

The second set of tutorials is based on the mathematics covered in the MATH 1046 course. Students may be familiar with some of this material from their high school linear algebra course. However, the content of these tutorials and the linear algebra course are much more in-depth than the high school level course. A short description of each of the algebra tutorials is listed below. To visit the tutorial, click the link below each description or the link from the menu on the left-hand side of the page.

# Vectors

The vectors tutorial begins with the basics of vectors and operations on them, such as addition, scalar multiplication, etc. It then gets into a more indepth discussion about dot and cross products, normalization, length, and lines and planes.

> | VECTORS tutorial

# System of Linear Equations

The systems tutorial gives several examples of systems and provides different methods to solve them. Methods are shown by solving several examples, and the tutorial also discusses concepts of linear independence and spanning sets.

> | SYSTEM OF LINEAR EQUATIONS tutorial

# Matrices

The matrices tutorial gives definitions and examples of various types of matrices. It then outlines operations on matrices, linear independence of matrices, transpose and inverse of a matrix, several theorems about matrices, and the Gauss-Jordan method for finding the inverse.

> | MATRICES tutorial

# Eigenvalues & Eigenvectors

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> | EIGENVALUES & EIGENVECTORS tutorial

# Orthogonality

The orthogonality tutorial discusses many topics linked with orthogonality. It outlines the difference between orthogonal and orthonormal, and discusses properties and theorems affecting orthogonal sets, matrices, complements and projections. It also goes through very important processes such as the Gram-Schmidt Process and QR Factorization. Many of the topics that are discussed have been generally mentioned in other tutorials, but is discussed more thorough in this tutorial.

> | ORTHOGONALITY tutorial

# Vector Space

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> | VECTOR SPACE tutorial

# Distance & Approximation

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> | DISTANCE & APPROXIMATION tutorial

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Alex Karassev