"Mathematics is not about numbers, equations, computations, or algorithms:

it is about understanding."
- William Paul Thurston (American mathematician)

Noel Evans, Ph.D. Page

Mathguy.us is happy to provide some of the works of Noel Evans, Ph.D. on this page. Dr. Evans graduated from the University of Texas at Austin in 1968 with a Ph.D. in Mathematics. Over the years, he has concentrated his work mostly on Math Education. Dr. Evans has written a number of books and many computer programs with an emphasis on Math Education. Mostly these explore possibilities in arithmetic and in Number Theory.

Dr. Evans taught at Angelo State University for 30 years, at Tulsa Junior College for 7 years and as a graduate student at University of Texas for several years. He also taught for 4 years (7th thru 12th grades) at Ambleside private school in San Angelo. Many of his papers were written while teaching at Ambleside.

Dr. Evans' approach to teaching Mathematics has been guided by the quote at the top of this page "The essence of mathematics is not to make simple things complicated, but to make complicated things simple." - Stanley Gudder (Professor of Mathematics, University of Denver). He is interested in making math more accessible, enjoyable and real-world related for students and others. We hope that you enjoy Dr. Evans' work as much as we do at mathguy.us.

Short Papers

In some of the papers below, negative numbers are expressed in bar notation. For example, -9 might be expressed as 9 with a bar over the 9. In these cases, the bar simply represents an alternative method for expressing a negative number and not that the digit or digits are repeating.

Mastering the techniques presented in these papers will make the student much more efficient in solving math problems. Even learning one or two of these techniques should improve the student's work. Use as many techniques as you can to save as much time you can.

• Subtraction by Subtracting First, Then Borrowing - An alternative that, with practice, can make subtracting large numbers easier. Very useful for subtracting numbers, for example, in a checkbook.
• Highest Common Factors Using Linear Combinations - A simple approach to finding Highest (Greatest) Common Factor (HCF or GCF) for two or more numbers.
• GCD and LCM for Fractions - An innovative approach that vastly simplifies the process of adding and subtracting fractions.
• Fractionease - Processes that will make adding and subtracting fractions easier. Can be used with number fractions and algebraic fractions.
• Solving Proportions Fast - Cross multiplication is good. This method is better.
• Polynomial Arithmetic - A method of performing operations on polynomials that is likely to significantly reduce the student's errors.
• Casting Out Nines: The Best Check - Save time checking your arithmetic operations by casting out nines.
• Checking Polynomial Operations by Casting Out Nines - Use the techniques in the "Casting Out Nines: The Best Check" paper to save time checking your operations with polynomials. Be sure to read "Casting Out Nines: The Best Check" before this one.
• Generalized Synthetic Division - Expands the use of synthetic division to the division of any two polynomials.
• Generalized Remainder Theorem - Find the remainder of a division of a polynomial by two or more factors easily. Also very helpful when evaluating polynomials at complex values.
• Partial Fraction Decomposition - Methods to speed up partial fraction decomposition. Especially useful when the decomposition involves numerous terms.