Course on Mathematics


The Math Course

For Course Tutor: Troubleshooting Math

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

SAT Prep

Algebra Cheat Sheet (full)
Algebra Cheat Sheet (reduced)

Level 3: Algebra Review
Level 4: Word Problem Review
Level 5: Practice Problems
Level 6: PSAT & SAT Review
Level 7: SAT Math (Khan Academy)

Arithmetic References

1885 Ray’s Practical Arithmetic
1893 Dubb’s Arithmetical Problems

Algebra References

Pre-algebra (Khan Academy)
Algebra 1 (Khan Academy)
Algebra 2 (Khan Academy)

Synthetic Division
Combinations and Permutations

Old Algebra Book
Paul’s Online Math Notes (Algebra)
1936 Coordinate Geometry (S L Loney)

Trig References

Trigonometry Cheat Sheet (full)
Trigonometry Cheat Sheet (reduced)

Trigonometry Index
Trigonometry (Khan Academy)
Paul’s Online Math Notes (Trigonometry)
1915 Plane Trigonometry (S L Loney)

Geometry References

High school geometry (Khan Academy)
Geometry—all content (Khan Academy)
Analytic Geometry—all content (Khan Academy)

Point and Unit
Old Geometry Book
Math Pages (Geometry)

Calculus References

Calculus Cheat Sheet

Calculus I
Calculus II
Calculus III
Differential Equations

Paul’s Online Math Notes
HMC Online Tutorials
Math Pages

Volumes by Cylindrical Shells
Double Integrals – Changing Order of Integration
Triple Integrals, Changing the Order of Integration, Part 1 of 3
Triple Integrals, Changing the Order of Integration, Part 2 of 3
Triple Integrals, Changing the Order of Integration, Part 3 of 3

Statistics References

Statistics Online
Math Pages

Mean, Median, Mode and Range
Quartiles, Boxes, and Whiskers
Five-number summary
Interquartile ranges and outliers
Standard Deviation

General References

Some Old Books
Purple Math
Common Core Math Standards


The Abacus and Numbers
Numbers & Consciousness
Going Beyond Counting
Point and Unit
Infinity and Unknowable
Comments on Infinity
Math Homonyms
Math Imitating Life
The Algebra of Unknowable
Fundamentals, Consistency and Breakthroughs
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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