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
| NOTATION & METHODS OF PROOF Tutorial
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
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
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
| 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.
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
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
> | MATRICES tutorial
Eigenvalues & Eigenvectors
| EIGENVALUES & EIGENVECTORS tutorial
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 tutorial
Distance & Approximation
| DISTANCE & APPROXIMATION tutorial
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