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- Arithmetic
- Algebra
- Geometry
- Trigonometry
- Calculus
- Test Prep for SAT, ACT, and GRE

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Jim is available for after school tutoring in the Hilltop area of Denver. You can contact him at

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or call 303-377-7960. Scheduling is on a first come basis with a 24 hr cancellation fee and a no-show charge.

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Euclid once told the Hellenistic Pharaoh Ptolemy “There is no royal road to geometry”. Math is one concept built upon another concept built upon another concept, et cetera, et cetera. A student of mathematics must walk the path, learning each concept along the way. When one concept is misunderstood it becomes difficult to build upon. This is why it only takes one bad math teacher to end a good student’s career in math. Even a few sick days can impede someone’s progress.

Sitting one on one with a student, a good tutor can watch the mistakes made and recognize which concepts the student has developed a poor understanding. This is called “filling in the holes”. As the student/mentor relationship develops a good tutor will learn how an individual student prefers to approach a problem and present explanations tailored to their conceptions. The two most obvious are the algebraic, step by step, process approach and the geometric, diagrammed, conceptualized approach. Most people fall into one of these two mindsets and generally one will excel in algebra and hate geometry while the other will love geometry and loath working through the algebra. Lastly, a good tutor can watch the expressions of the student and recognize when the proverbial light bulb turns on before moving on to the next subject.

When I draw a “3” on the board and ask if it is a number, people give me funny looks. The answer is no, “3” is not a number. It is a symbol that represents a number. When we as English speakers see “3” we think of a pattern we know as three. But when we see γ or ۳ we do not recognize them as three. The first is Greek and the second is Arabic. All these are numerals or symbols that represent numbers. Once people are freed from the rigid numerals numbers are easier to manipulate.

Mathematics is the study and description of patterns. Many people believe that math is the study of numbers. Numbers are so rich in patterns that they are necessary to describe other patterns. The description of patterns must be rigorous to qualify as mathematics. However, descriptions in simple language are sufficient to practice the art of mathematics.

Mathematics is the only art in the school of Natural Sciences. All other arts fall within the school of Liberal Arts. People think of mathematics as a science because each well posed problem has only one solution. However, from each question in math there are many different paths to the correct answer. One should choose the path that is most enlightening to their own mindset because everyone frames their own perceptions of basic mathematical patterns differently.

Most people look at this diagram and notice that there are many paths from a math question to the correct answer. Some paths are shorter than others and some are long and convoluted. One should avoid the long path because it takes a long time, it can lead to mistakes, and the long path usually isn't very enlightening.

The most interesting thing about having different paths to the answer is that the answer can be perceived in many different ways. For example, if the answer is “five” one can approach the answer as: 2+3, 1+1+1+1+1, half of ten, or any number of different ways. This may seem trivial in many regards, but it is how one can know they have the correct answer. Someone can look at a pencil, pick it up and spin it around, and say “yes, this is a pencil”. If you can get an answer using one approach, stop and look from another approach and get the same answer, then the answer is probably correct.

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**James Lowdermilk**

**Mathematician / Teacher / Tutor**

**EDUCATION**

BA Applied Mathematics Colorado State University, 1990

MA Applied Mathematics University of Montana, 1993

Thesis: “Pyramids and Whirlpools: Mathematical Models of Pyramid Building Techniques”

**PROFESSIONAL EXPERIENCE**

February 1994–December 1994: Land Info Inc. – Computer mapping/scanning/programming

March 1995 – present: Mathemagician Tutoring – Owner/operator

Fall 1998 – Fall 2009: Arapahoe Community College – Adjunct teaching including:

Preliminary Mathematics – Add/Subtract/Multiply/Divide/Fractions/Decimals

Finite Mathematics Intermediate Algebra College Algebra

Trigonometry Calculus

March 1999: Ancient Egypt Research Associates – Ground Penetrating Radar in Giza, Egypt

2008–2009: Vice President of Egyptian Study Society

2010–2011: President of Egyptian Study Society

2012–present: Member-at-Large on Board of Egyptian Study Society

**SCHOLARLY PAPERS**

Published in the Ostracon: Journal of the Egyptian Study Society

*The Monuments of Sneferu: The Bend in the Bent Pyramid and The Collapse of the Meydum Pyramid*, Spring 1999, volume 9, number 4

*The Inner-workings of the Egyptian Civil Calendar*, Summer 2000, volume 11, number 2

*Unit Fractions Inception and Use*, Summer 2003, vol. 14, number 2

*The Phoenix and the Benben: The Start of the Egyptian Calendar as the First Time*, Summer 2007, volume 18, number 1

*Year Counts in the Egyptian Calendar*, Winter 2012, volume 22, number 1

**PRESENTATIONS**

**University of Montana Dept. of Mathematics, December 9, 1993: “Pyramids and Whirlpools: Mathematical Models of Pyramid Building Techniques”**

Egyptian Study Society (ESS), February 22, 1994: “Pyramids and Whirlpools: Mathematical Models of Pyramid Building Techniques”

ESS, July 21, 1998: “Egyptian Mathematics: A Search for Early Mathematicians”

American Research Center in Egypt (ARCE) annual conference, April 23, 1999: “Calendrics and the Egyptian Unit Fraction”

ESS, October 19, 1999: “Libraries and Study in Ancient Egypt”

Arapahoe Community College, May 18, 2000: “Writing and Mathematics: The Chicken or the Egg”

ARCE annual conference, April 28, 2001: “A Commentary on the Study of Ancient Egyptian Mathematics”

ESS, October 15, 2001: “Sacred Knowledge”

ARCE annual conference, April 23, 2005: “The Development of the Egyptian Civil Calendar and its Effects on Society”

ESS, October 16, 2006: “On the Egyptian Calendar “

Mathematical Association of America, April 19, 2009: “From Pebbles to Precession”

ESS, June 16, 2008: “Greek Philosophers in Egypt”

ESS, February 16, 2010: “How to Create the 365-day Calendar”

ESS, November 19, 2012: “The Egyptian Calendar: A Simple Timeline”

**INTERESTS**

Mathematics and Astronomy / Egypt and Greece / Qi Gong / Tae Kwon Do

Telemark Skiing / Mountain Biking / Hiking / Family

Jim Lowdermilk has been the owner/operator of Mathemagician since 1995.

Established 1975.

Mathemagician offers professional tutoring for all levels of math including SAT/ACT/GRE preparation and Math, Algegra, Geometry, Trigonometry, and Calculus.

Contact This email address is being protected from spambots. You need JavaScript enabled to view it.

or call 303-377-7960