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Eclectic Homeschool Online Book Lists - Advanced Math and Calculus

This section of our website is devoted to book lists that you can take to your library. The lists are sorted by Category, Subcategory and then Topic.

Booklists Main Page > Mathematics

Advanced Math and Calculus List

  • Advanced Mathematics : An Incremental Development Solutions Manual
    by John H., Jr. Saxon
    ISBN: 1565770420
    2nd sol edition (June 1, 1997)
  • Advanced Mathematics: An Incremental Development: Home Study
    by John H., Jr. Saxon
    ISBN: 9992120649
  • Calculus for Cats
    by Kenn Amdahl (Author), Jim Loats (Author)
    ISBN: 096278155X
    This is a book for people about to take calculus, and for survivors of calculus who still wonder what it was all about. It gently explains the basic concepts and vocabulary without making the reader ever do a single problem.

    Even if you cringe at math, you'll enjoy the book's irreverent style and vivid imagery. A couple of hours from now, when you're done reading, you may be surprised that calculus no longer seems nearly so frightening
  • Calculus With Trigonometry and Analytic Geometry
    by Frank Wang, Diana Harvey, John H. Saxon
    ISBN: 0939798344
    (August 1988)
  • Calculus With Trigonometry and Analytic Geometry Solutions Manual
    by John Saxon
    ISBN: 0939798352
    (August 1988)
  • Calculus without Tears, Vol. 2: Newton's Apple
    by William Flannery
    ISBN: 0976413817
    This is the second volume in the series. It builds on the framework established in Vol. 1 to analyze the motion of a falling object, and continues toward the goal of the calculus of polynomials, which is reached in Vol. 3.
  • Calculus Without Tears: Easy Lessons for Learning Calculus for Students From the 4th Grade Up Vol. 1
    by William Flannery
    ISBN: 0976413809
    Our educational system keeps calculus shrouded in mystery - despite the fact that it was developed long long ago (in the 17th century) and it is the mathematical language of physics and engineering and hence the technological revolution that has transformed every aspect of our lives. Arguably it is mankind's greatest and most practical intellectual achievement.

    Why is it such a mystery? Calculus is taught 'theory first', that is, before a student studies calculus, he/she spends years studying abstract and difficult mathematics including geometry, algebra, and trigonometry. Here is a surprise: it's not necessary to know these subjects to learn calculus. Then the study of calculus itself is encumbered with the notion of mathematical proof, and the student is required to mathematically prove the simplest facts about calculus before actually 'doing' calculus.

    We could take the same approach to teaching arithmetic. First we would have a series of courses on symbolic logic. Then, as our arithmetic textbook we could use Whitehead and Russell's Principia Mathematica, an important work which proves the basic properties of arithmetic. Never mind that it is two thousand pages long and comes in 3 volumes. The definition of number is on page 234, and the proof that '1+1=2' is on page 362.Using this approach we would have to delay teaching multiplication until college. Fortunately, that's not the way arithmetic is taught. Unfortunately, it is the way calculus is taught.
  • Hands-on Trigonometry Proofs
    by Tessellations
    ISBN: B001UNXK3K
    This set contains four separate "proofs" of trigonometry relations, with examples of a Pythagorean identity, a sum formula, a double-angle formula, and two sum-to-product formulas. Demonstration of each relation is accomplished by physically rearranging the pieces to establish equalities of areas or lengths. These are not rigorous mathematical proofs, but rather visual common-sense proofs. As such, they help make these abstract relationships real and believable. By actually handling the pieces, students engage their minds to a greater degree than they would by merely looking at the proofs on paper. The color instructions describe how each proof is demonstrated, and four reproducible worksheets reinforce the material. Contains 20 magnetic foam pieces. Grades 7-12.
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