Course in Mathematics


Reference: Course on Subject Clearing


  1. What is Mathematics? (Video)
  2. Mathematics Overview (Video)
  3. Counting and Abacus (Video)
  4. The Concept of Numbers (Video)
  5. Math Diagnostics

For Parents with Young Children

Level 00: Pre-school Review
Level 0: Kindergarten Review

Earlier Gradients

Level 1: Primary School Review
Level 2: Middle School Review
Level 3: Pre-algebra (Khan Academy)
Level 4: Algebra 1 (Khan Academy)
Level 5: Algebra 2 (Khan Academy)

SAT Prep

Level 5: Algebra Review
Level 6: Word Problem Review
Level 7: Practice Problems
Level 8: PSAT & SAT Review
Level 9: SAT Math (Khan Academy)

For Course Tutor

Troubleshooting Math




  1. Combinations and Permutations
  2. 1885 Ray’s Practical Arithmetic
  3. 1893 Dubb’s Arithmetical Problems


  1. Algebra Cheat Sheet (reduced)
  2. Algebra Cheat Sheet (full)
  3. Synthetic Division
  4. Vertical and Horizontal Asymptotes
  5. Matching Polynomials with Graphs
  6. Inequality Problem
  7. Old Algebra Book
  8. Paul’s Online Math Notes (Algebra)
  9. 1895 Coordinate Geometry (S L Loney)


  1. Point and Unit
  2. Geometry—all content (Khan Academy)
  3. Analytic Geometry—all content (Khan Academy)
  4. High school geometry (Khan Academy)
  5. Old Geometry Book
  6. Euclid’s ELEMENTS
  7. Math Pages (Geometry)


  1. Trigonometry Cheat Sheet (full)
  2. Trigonometry Cheat Sheet (reduced)
  3. Trigonometry Index
  4. Trigonometry (Khan Academy)
  5. Paul’s Online Math Notes (Trigonometry)
  6. 1915 Plane Trigonometry (S L Loney)


  1. Calculus Cheat Sheet
  2. Paul’s Online Math Notes
    1. Calculus I
    2. Calculus II
    3. Calculus III
    4. Differential Equations
  3. Volumes by Cylindrical Shells
  4. Triple Integrals, Changing the Order of Integration, Part 1 of 3
  5. Double Integrals – Changing Order of Integration
  6. Triple Integrals, Changing the Order of Integration, Part 2 of 3
  7. Triple Integrals, Changing the Order of Integration, Part 3 of 3
  8. HMC Online Tutorials
  9. Math Pages


  1. Statistics Online
  2. Math Pages
  3. Mean, Median, Mode and Range
  4. Quartiles, Boxes, and Whiskers
  5. Five-number summary
  6. Interquartile ranges and outliers
  7. Standard Deviation

General References

  1. Some Old Books
  2. Purple Math
  3. Common Core Math Standards


  1. The Abacus and Numbers
  2. Numbers & Consciousness
  3. Going Beyond Counting
  4. Point and Unit
  5. Infinity and Unknowable
  6. Comments on Infinity
  7. Math Homonyms
  8. Math Imitating Life
  9. The Algebra of Unknowable
  10. Fundamentals, Consistency and Breakthroughs
  11. A Musical Interpretation of Pi


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  • Chris Thompson  On August 7, 2017 at 6:39 AM

    I remembered and looked up this humorous quote by Hubbard:

    “Rate of change is this mathematics known as Calculus. Calculus, it’s a very interesting thing, is divided into two classes — there’s Differential Calculus and Integral Calculus. The Differential Calculus is in the first part of the textbook on Calculus, and Integral Calculus is in the second part of the textbook on Calculus. As you look through the book, you’ll find in the early part of the book on Calculus, “dx” over “dy”, a little “dx”, and a little “dy” — and one’s above the other on a line — predominates in the front part of the book, but as you get to the end of the book you find these “dx” and “dy”s preceded by a summation sign, or are equating to a summation sign, and the presence of this shows that we are in the field of Integral Calculus.

    Now I hope you understand this, because I’ve never been able to make head nor tail of it. It must be some sort of a Black Magic operation, started out by the Luce cult — some immoral people who are operating up in New York City, Rockefeller Plaza — been thoroughly condemned by the whole society. Anyway, their rate-of-change theory — I’ve never seen any use for that mathematics, by the way — I love that mathematics, because it — I asked an engineer, one time, who was in his 6th year of engineering, if he’d ever used Calculus, and he told me yeah, once, once I did, he said. When did you use it? And he said I used it once. Let me see, what did you use it on? Oh yeah. Something on the rate-of-change of steam particles in boilers. And then we went out and tested it and found the answer was wrong.

    Calculus — if you want to know — there is room there for a mathematics which is a good mathematics. And it would be the rate of co-change, or the rate of change when something else was changing, so that you could establish existing rates of change in relationship to each other, and for lack of that mathematics, nobody has been able to understand present time — you just can’t sum it up easily — or let us say, for lack of an understanding of what present time was, nobody could formulate that mathematics. So, actually there’s a big hole there that could be filled — a thing called calculus is trying to fill that hole, right now, and it can’t.
    – L. Ron Hubbard

    I guess the week he spent at college didn’t turn out like he planned. The things he counts for knowledge, I can’t understand.
    (paraphrased from “Reeling in the Years.”)


  • vinaire  On August 7, 2017 at 8:43 AM

    Hubbard minimized whatever he could not understand. He minimized Buddha’s concept of Nirvana too. Nirvana has to do with attaining a viewpoint that is universal in nature and which looks at everything objectively.

    Hubbard misunderstood it to mean that, in Nirvana, the universe absorbs self and makes it MEST. That misunderstanding got him finally. He died fighting his imagined entities.


  • Anonymous  On November 17, 2017 at 11:09 AM

    this is davis


    • vinaire  On November 18, 2017 at 11:50 AM

      Welcome Davis. It is nice to see you here!


  • Anonymous  On September 21, 2019 at 11:23 AM

    I got your comment via email from Quora and Googled “Vinaire’s Blog” (since an actual link was not present). Your site looks very educational in certain areas. My site is more speculative, I think. My only reference to calculus is where I explain the Newton Raphson method for calculating roots. If you care to communicate, my email address is on my website. I couldn’t find yours here on this site.


    • vinaire  On September 22, 2019 at 4:29 AM

      Is this Gary Campbell from Quora? If you go to Quora, you will get the actual link. I shall write to you via email.


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