Patient math tutor, passionate about learning!

I've had lots of experience using math in business and in engineering. I'm also an adjunct professor at the Community College of Aurora, where I teach classroom courses in college algebra. If you're having difficulties with math, I've been there - math was my worst subject in high school. I got past the roadblocks and had fun doing it, and so can you! If you need a different way to look at things so you can "get it" or you need help with practice, give me a call.

Math should not be about memorization. At some point in the past, did you memorize the next sentence you're going to use? Probably not - you know what you want to say, and you construct the sentence or the phrase you need in order to say it. Once you get comfortable with math, it's just like talking ... you just "say" what you need to say, and that's it! After you learn it, math is fun. This approach requires two things - practice and patience. The best way to learn to talk this kind of math is by doing it - so let's dive in and talk math!

Finally, math is about more than just solving problems - it's about understanding and communication. Those who can "speak" math - who understand and can use the logic and the lingo - have a better chance at getting ahead in the world than those who can't. My goal is to help you find methods you can use to "translate" math problems into something you can understand, solve, and write down an answer for. These methods are usable not just for solving math problems you're dealing with right now, but can have an impact on your future in a variety of professions.

William's Subjects

Math:	ACT Math, algebra 1, algebra 2, calculus, discrete math, geometry, linear algebra, logic, prealgebra, precalculus, probability, SAT math, statistics, trigonometry
Test Preparation:	ACT Math, SAT math
Computer:	general computer, Microsoft Excel, Microsoft PowerPoint, Microsoft Word
Business:	Microsoft Excel, Microsoft PowerPoint, Microsoft Word
Corporate Training:	general computer, Microsoft Excel, Microsoft Word, statistics
Homeschool:	algebra 1, algebra 2, calculus, geometry, prealgebra, precalculus, SAT math, statistics

Algebra 1

Some say that algebra 1 is all about identifying and practicing techniques for setting up and solving problems that are "harder" than what you have to work with in arithmetic. This is at least partly true. The problems you encounter in algebra 1 are more challenging than those you encounter in arithmetic. However, you often use the same techniques you used in arithmetic to solve algebra 1 problems! So really, algebra 1 is a lot like the kinds of things you have already worked with - it just "looks"... Read More

Algebra 2

Algebra 2 is about identifying and practicing techniques for setting up and solving problems that are more challenging than what you had to work with in algebra 1. However, you often use the same techniques you're already familiar with to solve algebra 2 problems! So really, algebra 2 is a lot like the kinds of things you have already worked with - it just "looks" harder.

Algebra 2 topics include setting up and solving word problems, working with absolute value equations and inequalities,... Read More

Calculus

At the simplest level there are two types of calculus - differential calculus (analysis of derivatives) and integral calculus (analysis of integrals). For functions of the form y = f(x), differential calculus is often associated with rates of change, while differential calculus is typically associated with being able to find the area under a curve. At their base, both differential and integral calculus depend on the concept of "the limit", and on the concept of continuity.

Things in... Read More

Microsoft Excel

Microsoft Excel is a powerful spreadsheet program that is commonly used in a variety of professional (e.g. business, engineering, medical, and etc.) settings. Many people also use Excel at home, for a host of different tasks ranging from balancing checkbooks to maintaining address lists.

Like many successful software programs, Excel gets updated a lot. I've used various versions of Excel including 2003, 2004 (on a MacIntosh), 2007, and 2010 for a variety of business, engineering, and... Read More

Geometry

At the high school and beginning college levels, geometry can be divided into two basic categories: Coordinate geometry and plane geometry. If you're into more advanced mathematics you might be learning about something called non-Euclidean geometry - but that's a separate subject.

Generally speaking, coordinate geometry is about being able to compute values or find formulas associated with certain kinds of geometric objects - primarily lines and angles, various type of polygons (triangles... Read More

Prealgebra

Prealgebra is about word problems, knowing the correct order of operations for evaluating an expression, distance and time problems, relative scale problems, solving equations in one variable, understanding the basics of probability and basic geometry, and more!

Precalculus

Precalculus explores functions and equations that go beyond those you encounter in algebra 1. It expands on what you already know (or are at least aware of) about linear functions, quadratic / parabolic equations, factoring, circles, rational functions, inequalities, and etc.

Beyond the basics, ideas often encountered in precalculus include working with and graphing function inverses, exponential functions (including compound interest problems), and logarithms or logarithmic functions... Read More

Trigonometry

Some say trigonometry is all about understanding what are called "circular" functions ... that is, being able to work with the sine, cosine, tangent, cosecant, secant, and cotangent functions and their inverses. From my experience, it's a lot easier to understand and work with these functions if you pay attention to some basic concepts about circles, triangles, and the Cartesian coordinate plane. Some simple rules, the same kinds of things you learned in algebra 1, will help you through trigonometry... Read More

Statistics

A typical definition is "Statistics is the science of planning studies and experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data."

Basic descriptive attributes of data include the number of data values, plus the mean, median, mode, standard deviation, variance, range, quartiles, and etc. of the data. Given a set of data, these values are often easy to determine using a calculator or a software package... Read More

SAT Math

Topics covered in the SAT Math tests include basic arithmetic, algebra, geometry, and miscellaneous topics (mainly data interpretation and applied math). Hopefully, you should be comfortable with the types of problems you might see on the test by the 10th grade level.

The SAT Math tests have two main types of questions - problem solving (multiple choice) and student-produced responses (also called 'grid-ins'). For the problem solving questions you get one point for every correct answer... Read More

Probability

Probability is closely related to statistics. In fact, at the introductory levels, probability and statistics are often taught as a single class. One of the key differences is that statistics relies on having data; you use the data to compute values associated with mean, standard deviation, and etc. With probability, you can create a theoretical distribution (which may or may not be based on attributes of collected data) that you believe is a good model for the types of outcomes you might expect... Read More

ACT Math

ACT Math covers the following subjects: Prealgebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry, and trigonometry. You'll have 60 questions you'll want to answer over 60 minutes. You can use standard calculators to answer these questions, although you're not allowed to use some types of calculators (e.g. you can't use the TI-89 or the TI-92 to check your answers on this test).

There are practice tests you can use to help you do better when you take... Read More

Linear Algebra

Linear algebra (generally associated with analysis and solution of systems of linear equations) is used in a variety of engineering and business applications. Some examples of how I've used linear algebra in my personal experience include:
* Linear algebra is an essential component of least squares data reduction processing and covariance analysis, used in probability and statistics. In a variety of engineering and business applications, the ability to use probability and statistics is critical... Read More

Read all subject qualifications »

Education

University of Washington Department of Economics (Mathematics) Colorado Technical University (Master's)

Powerful Teacher — I was very impressed with William and his ability to get my son's attention and engage him in logical discussions. William also quickly assessed our son's abilities and pinpointed strengths and weaknesses almost immediately. He addressed challenges I have had for years in reaching my son, within a few minutes of starting the lesson. William has a captivating way of relaying information to the point ...

— Jennie from Aurora, CO

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William will travel within 15 miles of Aurora, CO 80013.

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