What you get: personalized attention and small classes; step-by-step, logical methods; focus on how and why, not just the what (not just content); confidence and subject mastery; a solid education in reasoning and thinking skills; an expert instructor who knows more than just the math, who brings in science, history, law, literature, and logic.

 

Arithmetic

Course description: we will cover the concepts of arithmetic in each sequence with stress on practical application, deriving concepts, as much as possible, from real-life examples, and reasoning things out. We will make sure students know how and why something is true. This is critical for higher mathematics, science, finance, accounting, household calculations, and more. We will cover addition, subtraction, multiplication, division, and more, as appropriate for the age group.

Possible texts:

1.  Ray’s Arithmetic by Joseph Ray, available online through various sources such as Mott Media, or free on sites such as Google Books

2.  Singapore Math

 

Algebra 1   Buy now.

Course description: we will cover the concepts of algebra with stress on how we know things and on practical application, which are the more important things to get out of algebra. Learning derivations and explanations of algebraic concepts teaches us how to reason and gives us confidence in our ability to understand; not learning the derivations and explanations short-circuits the mind, keeps students from developing the ability to think critically, intelligently, and imaginatively, and stifles their self-confidence. We will cover the real numbers, algebraic expressions, linear equations in one and two variables, systems of equations, inequalities, polynomials, functions, exponents, powers, roots, quadratic equations, rational expressions/equations, radical expressions/equations, and graphing. Time permitting, maybe also other topics like the conic sections, exponential functions, logarithmic functions, probability and statistics.

Possible texts:

1.  Introductory Algebra By Keedy & Bittinger, Addison-Wesley Publishing Company, (c) Addison-Wesley Publishing Company, Inc.

2.  Elementary Algebra by Larson & Hostetler, Houghton Mifflin Company, (c) Houghton Mifflin Company

3.  Algebra: Structure and Method by Dolciani, Brown, Ebos & Cole, Houghton Mifflin Company, (c) Houghton Mifflin Company

 

Algebra 2   Buy now.

Course description: we will cover the concepts of algebra with stress on how we know things and on practical application, which are the more important things to get out of algebra. Learning derivations and explanations of algebraic concepts teaches us how to reason and gives us confidence in our ability to understand; not learning the derivations and explanations short-circuits the mind, keeps students from developing the ability to think critically, intelligently, and imaginatively, and stifles their self-confidence. We will cover the real numbers, linear equations, systems of equations, matrices, inequalities, polynomials, functions, rational expressions/equations/functions, exponents, powers, roots, quadratic equations, complex numbers, graphing, the conic sections, exponential functions and logarithmic functions. Time permitting, maybe also other topics like sequences, series, and probability and statistics.

Possible texts:

1.  Intermediate Algebra By Keedy & Bittinger, Addison-Wesley Publishing Company, (c) Addison-Wesley Publishing Company, Inc.

2.  Algebra 2 by Hall & Fabricant, Prentice Hill publishers, (c) Prentice-Hall, Inc.

3.  Intermediate Algebra by Cynthia Young, John Wiley & Sons publishers, (c) John Wiley & Sons, Inc.

4.  Intermediate Algebra by Larson & Hostetler, Houghton Mifflin Company, (c) Houghton Mifflin Company.

 

Geometry   Buy now.

Course description: we will cover the concepts of geometry with stress on how we know things, on proof, and on practical application, which are the more important things to get out of geometry (more important than just memorizing formulas or doing algebra). They teach us how to reason, which is something we can and should take with us in all areas of life. Formulas we can look up in books or on our computers. Of course, we cannot learn the “how” or learn proof without knowing any content. We will cover all the elements of classic geometry: triangles, parallel and perpendicular lines, polygons, area, perimeter, circles, arcs, proportion, similarity, trigonometry, axioms, constructions.

Possible texts and workbooks:

1.  Geometry by Jurgensen, Jurgensen & Brownm, McDougall Littel publishers, (c) Houghton Mifflin Company

2.  Geometry for Enjoyment and Challenge by Rhoad, Milauskas, and Whipple, McDougall Littel puslishers, (c) McDougall, Little & Company

3.  Polygons by Steck-Vaughn School Supply (Harcourt Publishers), ISBN 0-7398-2931-9

4.  Solids by Steck-Vaughn School Supply (Harcourt Publishers), ISBN 0-7398-2932-7

5.  How To Succeed in Geometry by Teacher Created Resources, ISBN 978-1-57690-958-4

6.  Measurement & Geometry by Steck-Vaughn School Supply (Harcourt Publishers), ISBN 1-4190-0437-9

 

Precalculus

Course description: we will consider precalculus for what it is: a development of algebra and geometry, and we  will learn derivations and explanations of concepts to teach students how to reason and to give them confidence in their ability to understand. Not learning the derivations and explanations short-circuits the mind, keeps students from developing the ability to think critically, intelligently, and imaginatively, and stifles their self-confidence. The course will include functions, graphing, trigonometric functions, applications of trigonometry, trigonometric identities, trigonometric equations, polynomial functions, inequalities, exponential functions, logarithmic functions, polar coordinates, conic sections, matrices, sequences, and series. Time permitting, maybe also other topics like probability, statistics, three-dimensional vectors, matrix transformations, and limits.

Possible texts:

1.  Precalculus by Foerster, Key Curriculum Press, (c) Key Curriculum Press

2.  Precalculus Mathematics by Demana, Waits, & Clemens, Addison-Wesley publishers, (c) Addison-Wesley Publishing Company, Inc.

3.  Advanced Mathematics: A Precalculus Approach by Ryan, Doubet, Fabricant & Rockhill, Prentice Hall publishers, (c) Prentice-Hall, Inc.

4.  Trigonometry by Smith & Hanson, Word Book Company Publishers, (c) World Book Company

5.  Trigonometry Refresher by Klaf, Dover Publications, (c) A. Albert Klaf

 

Calculus

Course description: we will develop calculus from its geometric and physical bases. Calculus is a very practical subject — it was developed to solve problems in physics and astronomy — and should be taught accordingly. This can be taught as a one or two year course, depending on the depth and course content one wants to cover. The course will include (depending on scope and content needed) limits, continuity, derivatives, integrals, exponential and logarithmic functions, transcendental functions, techniques of integration, indeterminate forms, improper integrals, infinite series, analytic geometry, plane curves, polar coordinates, vectors, solid geometry, vector-valued functions, partial derivatives, multiple integrals, vector calculus, differential equations.

Possible texts:

1.  Calculus by Swokowski, Prindle, Weber & Schmidt publishers, (c) PWS Publishers

2.  Calculus by Larson, Hostetler, & Edwards, D. C. Heath and Company, (c) D. C. Heath and Company

 

Probability & Statistics

Course description: we will start from the inductive basis of statistics and work our way into statistics proper. Satistics is based in induction and categorization, and hence we should start there. We will cover statistical measures of data, statistical description of data, probability, graphing, distributions of random variables, discrete and continuous probability distributions, the normal distribution, sampling theory, experiments, estimation of parameters, confidence intervals, tests of hypotheses, regression and correlation. Time permitting, maybe also other topics like analysis of variance, chi-square tests, and nonparametric statistics.

Possible texts:

1.  Elementary Statistical Concepts by Walpole, Macmillan Publishing Co., Inc., (c) Ronald E. Walpole

2.  Introduction to Statistics by Walpole, Macmillan Publishing Co., Inc., (c) Ronald E. Walpole

3.  Intro Stats by DeVeaux and Velleman, Addison-Wesley publishers, (c) Pearson Education, Inc.

4.  The Practice of Statistics by Yates, Moore, & McCabe, W. H. Freeman and Company publishers, (c) W. H. Freeman and Company

 

Physics

Course description: we will cover physics from an inductive, historical perspective, taking two years to cover the subject. It is important for students to learn how and why scientists developed the ideas and theories they did; today, most science is taught as coming out of nowhere and being true just because the teacher or book says so — not at all how any science should be taught. Science should be taught as science has been done: starting with the evidence of the senses, and developing concepts, propositions, principles, explanations, and theories step by step from there. We should follow the actual method of the scientists of the ages, something studied most successfully and most recently by the philospher-physicist David Harriman of Falling Apple Science. We will cover Aristotle, Euclid, Ptolemy, Copernicus, Tycho Brahe, Kepler, Galileo, Newton, Fahrenheit, Rumford, Mayer, Joule, Helmholtz, Snell, Roemer, Michelson, Gilbert, Franklin, Cavendish, Coulomb, Galvani, Volta, Ohm, Thomson, Oersted, Ampere, Faraday, Plank, Einstein, Rutherford, Maxwell, learning about the roots and development of ancient astronomy, modern astronomy, motion, force, gravity, statics, optics, fluids, energy, power, collisions, sound, heat, electrostatics, electrochemistry, electric circuits, magnetism, electromagnetism, light, the atomic theory of matter, x-rays, radioactivity, atomic spectra, the atomic nucleus, nuclear fission and fusion. Time permitting, maybe also other topics like systems of particles, rotation, interference and diffraction, entropy, and relativity.

Possible texts, books, and readings:

1.  Physics by Tipler, Worth Publishers, Inc., (c) Worth Publishers, Inc.

2. Physics by Halliday & Resnick, John Wiley & Sons publishers, (c) John Wiley & Sons, Inc.

3.  Fundamentals of Physics by Halliday & Resnick, John Wiley & Sons publishers, (c) John Wiley & Sons, Inc.

4.  Two New Sciences by Galileo Galilei, trans. Crew & Alfonso, Dover Publications, Inc.

5.  Discoveries and Opinions of Galileo, trans. Stillman Drake, Doubleday Anchor Books, (c) Stillman Drake

6.  Selections from Aristotle, at The Internet Classics Archive

7.  On the Revolutions of the Heavenly Spheres by Copernicus

 

Chemistry

Course description: we will cover chemistry from an inductive, historical perspective. It is important for students to learn how and why scientists developed the ideas and theories they did; today, most science is taught as coming out of nowhere and being true just because the teacher or book says so — not at all how any science should be taught. Science should be taught as science has been done: starting with the evidence of the senses, and developing concepts, propositions, principles, explanations, and theories step by step from there. We should follow the actual method of the scientists of the ages, something studied most successfully and most recently by the philospher-physicist David Harriman of Falling Apple Science. We will cover Roger Bacon, Bernard Trevisan, Theophrastus Bombastus (Paracelsus), John Becher, Roberty Boyle, Joseph Priestley, Henry Cavendish, Antoine Lavoisier, John Dalton, John Berzelius, Amedeo Avogadro, Freidrich Woehler, Dmitri Mendeleeff, Savante Arrhenius, Marie Curie, Joseph Thomson, Henry Moseley, Irving Langmuir, and more; learning about the roots and development of alchemy, chemistry, the theory of gases, the theory of matter, atomic theory, atomic structure, the periodic table, chemical reactions, stoichiometry, thermochemistry, bonding, solutions, chemical kinetics, electrochemistry, acids and bases. Time permitting, maybe also other topics like organic chemistry and biochemistry.

Possible texts, books, and readings:

1.  Chemistry: The Central Science by Brown, LeMay, Burdge & Bursten, Pearson Education publishers, (c) Pearson Education, Inc.

2.  Chemistry by Zumdahl & Zumdahl, Houghton Mifflin publishers, (c) Houghton Mifflin Company

3.  Chemistry by Mortimer, Wadsworth Publishing Company, (c) Wadsworth, Inc.

4.  Crucibles: The Story of Chemistry by Jaffe, available on The Internet Archive and Google Books

5.  Crusaders of Chemistry by Leonard, available on The Internet Archive and Google Books

6.  The Golden Book of Chemistry Experiments by Brent, Golden Press Publishers, (c) Golden Press, Inc., availble for on About.com

 

SAT/ACT Prep

Course description: we will cover the layout and format of the test, the content that will be tested, test strategies, and more.

Possible texts, books, and readings:

1.  The Official SAT Study Guide, The College Board publishers, (c) The College Board and Educational Testing Service

2.  10 Real SATs, Henry Holt and Company LLC publishers, (c) College Entrance Examination Board and Educational Testing Service

3.  10 SATs, College Board publishers, (c) College Entrance Examination Board

4.  Cracking the SAT by Robinson & Katzman, Random House publishers, (c) The Princeton Review, Inc.

5.  Reading and Writing Workbook for the SAT by Martz & Pierce, Random House publishers, (c) The Princeton Review, Inc.

6.  The Unofficial SAT Word Dictionary by Burchers, Burchers, & Burchers, New Monic Books publishers, (c) Sam Burchers

7.  The Real ACT Prep Guide, Thomson Peterson’s publishers, (c) ACT, Inc.

8.  Cracking the ACT by Martz, Magliore, & Silver, Random House, Inc., publishers, (c) The Princeton Review, Inc.

9.  McGraw-Hill’s ACT by Dulan, McGraw-Hill publishers, (c) The McGraw-Hill Companies, Inc.

10.  Rex Barks by Davenport, Paper Tiger Publishers, (c) Phyllis Davenport