High School Topics

  • Functions (definition, odd, even)
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  • Basic Algebra
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  • Geometry
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  • Trigonometry
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  • The Quadratic Function
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  • Polynomials (e.g. division and remainder theorem)
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  • Binomial Theorem
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  • Logarithms
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  • Exponential and Natural Log Functions I
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  • Limits I
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Calculus

  • Curve Sketching I
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  • Inverse Functions
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  • Newton's Method of Approximating Roots
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  • Series
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  • Probability I
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  • Statistics II
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New topics continue to be added. Check back every few weeks if your topic of interest has not yet been added. Also please excuse any glitches, as I am actively developing. Bookmark the page and revisit weekly to see what's been added/changed. Questions can go to p.cao@student.unsw.edu.au. -22 Jan 2011.

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If you are a returning visitor, please refresh your browser on return, to update any cached data, since the website may have changed since your last visit. Similarly, if math symbols appear distorted, simply refresh your page.

New Topics Released

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Updates

  • 6 Aug 2011 A new topic, Population Modelling has been introduced and one subtopic Logistic Growth, as been added.
  • 2 July 2011 Forum development has been put on hold due to technical difficulties.
  • 19 Feb 2011 - 1 subtopic has been added to Probability I (total of 7/8 subtopics complete now)
  • 10 Feb 2011
  • 2 Feb 2011 - 1 subtopic has been added to Probability I (total of 6/8 subtopics complete now)
  • 31 Jan 2011 - 1 subtopic has been added to Probability I (total of 5/8 subtopics complete now)
  • 27 Jan 2011 - 1 subtopic has been added to Probability I (total of 4/8 subtopics complete now)
  • Previously - 1 subtopic have been added to Probability I (total of 3/8 subtopics complete now)
  • Previously - 1 subtopic have been added to Probability I (total of 2/8 subtopics complete now)
  • Previously - 1 subtopic have been added to Probability I (total of 1/8 subtopics complete now)
  • Previously -1 subtopic has been added to Differentiation (total of 1/? subtopics complete now)
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Tips for using the site:

  • The roman numerals (I, II) which feature in the title of some topics indicate that the same topic title recurs and is extended on in university.
  • The cutoff for where highschool topics end and university topics begin is somewhat arbitrary and will vary from country to country and even from state to state. So if you are studying on the boundary of high school and university and you can't find a certain subtopic which you feel ought to have been covered, check out the alternate half of the site.
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  • This site uses the latest technology available to typeset beautiful math.
  • If you value this site, please consider donating, to ensure it always stays viable. At the moment, the running costs are entirely on me. I also have to give up much of my time to design, develop and write content for this site, during which time I haven't been earning a living. How many people in the world would go to such pains to make math free and accessible? Please support me - click donate below:

General math tips:

  • If you can derive a formula from first principles and you experience a mental blank in an exam, you can always derive it on the spot! Not all derivations are simple however, or intuitive.

As of the end of Probability I, I will commit to adding a new topic for every $10 donated. When you donate, you can nominate what topic will be written from the list of topics running down either side of the home page. It must fall within the scope of the topics listed and be expected to be no more advanced than typical 1st-year uni/college. Note that almost all of high school probability and part of high school differentiation have already been written. Either use the special instructions in the donation tool, email me at p.cao@student.unsw.edu.au, or leave it open-ended and I'll commit to a topic of my choice. The topics will be written in the same style as Probability-1, and uploaded to the site once I am done. This is the only way I'm going to be able to pay off site hosting and expensive software fees. When I started this site, I envisaged that donations would come freely, and advertising would absorb costs. Not so! I'm finding myself out of pocket here. So if you like what you see and you want to see more, please consider donating! (Donations received so far: $0.)


Say NO to Adsense. Adsense has decided against the community and educational spirit to deny this site the chance to remain financially viable. They have rejected all my attempts to explain innocent incidences of invalid clicks. Particularly in the light of this site's pro-educational and not-for-profit stance, I consider that Adsense has been unjust and corporate-like in their dealings with the teacher and student community. I will be happy to take down this boycott notice and accept their services once again if Adsense are willing to lift their ban on this site. I am only asking on behalf of the community as I do not profit and in fact make a loss on this site, to deliver quality educational material for free. Please think twice Adsense, and heed our plea. If you are reading this Adsense please email me at p.cao@student.unsw.edu.au in a helpful spirit to resolve this.


Disclaimer: It's important to check with traditional sources for correctness, such as your textbook or your teacher. And don't assume I am right 100% of the time! If you spot an error tell me about it at p.cao@student.unsw.edu.au and it will be fixed.

© Peter Cao 2010

University Topics

  • Number Systems and Set Notation
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Calculus

  • Limits II
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  • Implicit Differentiation
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  • Partial Differentiation
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  • Reduction Formulae
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  • Mean Value Theorem
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  • Curve Sketching II
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  • L'Hôpital's Rule for Limits of Indeterminate Form
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  • Integration by Parts
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  • Integration by Trigonometric Substitution
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  • Exponential and Natural Log Functions II
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  • Ordinary Differential Equations (ODEs), First Order
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  • Ordinary Differential Equations (ODEs), Second Order
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  • Series to Infinity
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  • Taylor Polynomials
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  • Taylor Series
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  • Graphs in R3
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  • Total Differential Approximation
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  • Hyperbolic Functions
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Algebra

  • Complex Numbers
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  • Vectors
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  • Matrices
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  • Linear Transformations
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  • Eigen Values and Eigen Vectors
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