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Review and Remedial Mathematics Mini-Courses

If you are planning to take a college-level math course (such as precalculus, calculus or discrete math) after having been out of touch with mathematics for a number of years, you might benefit from review-tutoring or remedial tutoring that will help you regain, strengthen and supplement your basic math skills. And if you experience a particular anxiety with respect to math, then it is likely that the review should cover not just the standard topics in arithmetic and algebra - such as computing with fractions or solving linear equations - but, first and foremost, fundamental skills such as understanding and using mathematical symbols, using variables, dealing with various levels of abstraction, approaching math problems without fear, grasping and using algebraic laws, and being able to read and comprehend a math textbook.

I specialize in giving you precisely the kind of review or remediation you need. To this end, besides standard open-ended tutoring arrangements, I offer three types of fixed-price mini-courses designed to help you prepare for college math classes. They are all strictly one-on-one, and all the "live" sessions and written communications are entirely tailored to your specific needs and difficulties. Which of these mini-courses (if any) is right for you is a decision you and I make jointly on the basis of your answers to a special Math-Review Assessment Sheet. You can download the Assessment Sheet in either MS Word (.doc) format or PDF format.

All three mini-course types share the following features:

  • They are designed to make you proficient in the topics which are listed below on this page.

  • I ask you to purchase two (cheap) books, Schaum's Outline of Elementary Algebra by by Barnett Rich and Philip Schmidt, and Schaum's Outline of Intermediate Algebra by Ray Steege and Kerry Bailey. These serve as the ground reference texts for all three mini-courses.

  • Throughout each mini-course, I supply you with a wealth of additional, specially written materials that permit you more practice, target your weak areas, integrate understanding and doing, give better explanations or different perspectives, and generally strengthen your grasp of the subject.
Within these common parameters, the three types of mini-course options I offer are as follows:
  1. Assisted Self-study Brushup. This is the recommended course if you are able to study on your own and experience no major trouble areas. You study the books and the extra materials I supply you with, do the problems, and send them to me for review. I review them and send you back corrections and fully explanatory comments. Price: $150.

  2. 10-session Review. This is the recommended course if you are able to study on your own and can read and interpret algebraic formulas, but experience some significant gaps or trouble areas. Includes everything that is included in the Assisted Self-study Brushup course, but in addition you get 10 hours of specially targeted "live" one-on-one tutoring sessions. Price: $300.

  3. 18-session Remedial. This is the recommended course if you have trouble with math-reading comprehension, need to boost your ability to study by yourself, and/or require remedial work in using the language of arithmetic and algebra. Includes everything that is included in the Assisted Self-study Brushup course, but in addition you get 18 hours of specially targeted "live" one-on-one tutoring sessions. Price: $500.
All mini-courses, irrespective of type, cover the following topics:
Understanding and creating arithmetic and algebraic expressions and sentences. Variable substitution.

Number systems: natural numbers, integers, rational numbers, real numbers. Representations of numbers (decimal notation, fractions, etc.)

Arithmetic operations and their order. Addition, subtraction, multiplication, division, raising to a power, taking roots. Some basic laws governing these operations.

Integers: Even and odd, prime and composite. Prime factorization. Divisibility: quotient and remainder. Least common multiple, greatest common divisor.

Order relations between numbers.

The real number line. Bounded and unbounded intervals.

The concept of additive and multiplicative inverses. General laws governing numeric operations.

Absolute value.

Properties of inequality. Solving inequalities, including absolute-value inequalities.

Exponents: natural number exponents, integer exponents. Radicals. Simplifying radical expressions. Fractional exponents.

Cartesian coordinates on a plane. Plotting points. The Pythagorean Theorem. The distance formula.

Linear equations and linear inequalities; their properties. Solving them algebraically.

Different ways of specifying a straight line: point slope, slope intecept, etc. Parallel and perpendicular lines. Solving linear equations graphically.

Quadratic equations and methods to solve them algebraically.

Polynomials. Arithmetic operations on polynomials. Rational expressions.

If you are wondering which learning approach is best for you - an open-ended tutoring arrangement or one of the above types of mini-courses - you might want to download and answer the Math-Review Assessment Sheet which helps me guide you in choosing a proper tutoring strategy. You can download the Assessment Sheet in either MS Word (.doc) format or PDF format. My review of your answers to this Sheet and my recommendation of a suitable tutoring plan are, of course, free of charge.