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The art of teaching is the art of assisting discovery.
Mark Van Doren

If you can't explain it simply, you don't understand it well enough.
Albert Einstein

Any fool can know. The point is to understand.
Albert, again.

Function analyzer: wims.unice.fr

Millersville University:final-review sheets & solutions for Basic Algebra, Trigonometry, Calculus 1, 2 & 3 .

JUST THE MATHS: From Algebra to differential equations: Teaching Units.Table of content. By A. J. Hobson.

MATHISPOWER4U tutorials: Algebra, Calculus I, II, III, differentail eq, set theory, logic, etc.


NC State University:

Harvard Univ:

Math21a, Multivariable Calculus by Prof O. Knill.

Community Calculus: Whitman College, ebooks:

  • Single variable calculus, early transcendentals, in PDF format.
  • Multivariable calculus, early transcendentals, in PDF format.‏

Mathematics Multimedia Center Recorded Lectures

Prof. R. Delaware, Kansas' Univ. College Algebra

Calculus I Lectures, NYU. Prof. M. Leingang.


Multivariable Calculus by Prof. Evans Lawrence.

Calculus 3 lectures, prof. Tavis Kowalski.

Millersville University:
Calc III reviews
1, 2 & 3; final review.

Formula and Theorem Review. Tommy MacWilliam, Harvard College. Or download it here.

Proof of the magnitud of the cross product by S. Surgent.

Grad, Div & Curl: in real life.
By Open University:

Volumes of Solids of Revolution, Loyola Univ, Maryland.

Linear aproximations: by S.O.S Math

Summary of conic sections, Stewart

Area of a surface of revolution, Stewart.

University of Huston, Mathematics help

Polar graphs

Desmos Graphing Calculator (online)
Online graphing calculator from desmos.com

Draw function graphs

Graphics for Complex Analysis

Complex Function Grapher

Investigating Parent Functions

WIMS.unice.fr: Matrix calculator


Probability, Mathematical Statistics, Stochastic Processes. University of Alabama in Huntsville.

Probabilitycourse.com by H. Pishro-Nik:
University of Massachusetts Amherst.

Finite Mathematics N.C. State University
(Matrices, Sets & counting, probability).

Stat using Graphing Calculators

fx-115 ES Plus: youtube video, min 40: stat

Casio CFX-9850 Plus and CFX-9750 Statistics

TI-83 & TI-84 Tips for Statistics by NapaValley.edu

Virtual TI 83:

Download compressed folder (windows zip):

Logic: the structure of reason


Online notes:

The OPEN textbook LIBRARY: the most complete source of free textbooks in the world wide web !! (pdf download, again, for free). Algebra, Linear Algebra, Calculus, Statistics, Abstract Algebra, Number Theory etc ...

Paul's Online Math Notes http://tutorial.math.lamar.edu/

Professor Paul Dawkins website covers his classes: Algebra (Math 1314), Calculus I (Math 2413), Calculus II (Math 2414), Calculus III (Math 2415) and Differential Equations (Math 3401). Professor Dawkins teaches at Lamar University, Texas.

** By WolframMathWorld.com: A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by:

1. Summary of Convergence Tests for Series with examples, pdf.

2. Convergence tests for Series: flowchart, pdf.


The normal distribution:

Statistics Learning Centre

Mth120 - Statistics I at Elgin Community College

The University of Alabama in Huntsville: Random
Probability, Mathematical Statistics, Stochastic Processes


Introductory Statistics, Vol 1: textbookequity.org

Introductory Statistics, Vol 2: textbookequity.org

Collaborative Statistics, pdf download, by Barbara Illowsky PhD.

Introduction to Probability, Dartmouth College: 1. Ebook; 2. Solutions.

1. Stat Trek, Teach yourself statistics: http://stattrek.com/

2. Summary of confidence interval and hypothesis testing formulae by Duquesne University Math Dept.

3. Online Statistics Education: An Interactive Multimedia Course of Study Developed by Rice University (Lead Developer), University of Houston Clear Lake, and Tufts University

4. University of Texas: Virtual Laboratories in Probability and Statistics

5. Statistics Tables, online: University of Central Florida

6. Statistics Formulas by Mario F. Triola Copyright 2010 Pearson Education.

7. Statistics Tables by Mario F. Triola Copyright 2010 Pearson Education.

*Complete set of formulas and tables, by Mario Triola*

+another set of stat formulas+

8. Student's t distribution table, pdf, by scholar.vt.edu

Also: Important Formulas card, from Essentails of Business Statistics by Bowermann & O'Connell.
Direct download here.

9. F tables: There is an F table for each alpha (right tail). The rows represent denominator degrees of freedom and the columns represent numerator degrees of freedom.
Most hypothesis testing problems avoid left tailed tests. Sometimes, however, the left F critical value is needed. If you have a calculator --like Casio fx 9750 or 9860, then go to Dist, F, InvF, enter 1-alpha or 1-alpha/2,-for one tailed or two tailed tests, respectively; and the degrees of freedoms: numerator(n:df), denominator (d:df). See right tail areas, by UCLA.

10. Confidence Interval for One Variance:

Casio graphing calculator: Distributions, CHI, InvC. Area: alpha/2 and 1-alpha/2; df=n-1.

11. Confidence Interval for the Ratio of two Variances:

The confidence interval provides a range of likely values for the ratio between two population variances or standard deviations. If the confident interval contains one, we cannot conclude that the population’s variances differ.  It is given by:

Finding F  critical values: 

Casio graphing calculator: Distributions, F, InvF:  for F alpha/2, Right tail, enter the alpha/2, for Area; then the numerator df, followed by the denominator df. (Recall, the larger variance goes on the numerator).

For the left tail, enter the 1-alpha/2 value for area, and numerator df, denominator df.

Note: images created online at codecogs/editor/latex/eqneditor.php

10. The Analysis ToolPak is an Excel add-in program that provides data analysis tools for statistical data analysis. It is specially useful for one way ANOVA and two way ANOVA analysis, correlation and regression analysis.
Tutorial here created by Excel easy #1 Excel tutorial on the net
ALSO Real Statistics using Excel, by Dr. Charles Zaiontz, excelent site !

...find here an excel file.

Understanding Public Opinion Survey
by MichiganSc.

Designing an Experiment, Power Analysis by Statsoft.com

"Performing power analysis and sample size estimation is an important aspect of experimental design, because without these calculations, sample size may be too high or too low. If sample size is too low, the experiment will lack the precision to provide reliable answers to the questions it is investigating. If sample size is too large, time and resources will be wasted, often for minimal gain. "

Java applets for power and sample size by statsoft.com

Power tables (Cohen, 1988) pdf.

Power analysis: Effect size formulas, by UCLA.

Probability: The Deck of Cards.

A deck of cards consists of 4 suits, 13 cards each for a total of 52 cards. The four suits are: Spades, Hearts, Diamonds, and Clubs. Each suit contains an A (Ace), numbers from 2 to 10, and three face cards: J, The Jack; Q, the Queen and K, the King.
Colors: Hearts and Diamonds are red, Spades and Clubs are black.

Spades, Hearts, Diamonds, Clubs:


Statistical Intervals. Tolerance intervals.

A tolerance interval is a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls (source, Wikipedia).

* You might want a tolerance interval by Mark J. Nelson

* Understanding Statistical Intervals: Part III - Tolerance Intervals by ProPharma Group

* Values of k for Two-Sided Intervals

Confidence Levels and Hypothesis testing:

**Summary of confidence interval and hypothesis testing formulae** by Duquesne University Math Dept.


ANOVA table:

One-way ANOVA
Source of Variation SS df MS F
Between Groups SSB k-1 MSB=SSB/df F=MSB/MSW
Within Groups SSW n-k MSW=SSW/df
Total SST=SSB+SSW n-1    

SSB(between) =SST(treatments)
SSW (within)= SSE (residual errors)
Total sum of squares=Treatments sums of squares + sum of squares of the residual error.

Two way ANOVA
Source of Variation SS df MS F
Factor A SSA a-1 MSA=SSA/df MSA/MSE
factor B (blocks) SSB b-1 MSB=SSB/df MSB/MSE
Error SSE (a-1)(b-1) MSE=SSE/df
Total SST=SSA+SSB+SSE n-1    

SSB, sum of squares due to blocks: the sum of the squared differences between block means and the overall mean, multiplied by k, the number of treatments.

Critical Values for the Tukey Q Test, alpha = .05 click here

ANOVA regression: df SS MS F
Regression 1 SSR MSR=SSR/df MSR/MSE
Residual n-2 SSE MSE=SSE/df
Total n-1 SST=SSR+SSE    

Regression df: number indep vars (IP).
Residual df: number of data points(observations)-num ip-1. Simple linnear reg df=n-2; multiple linear regression: n-ip-1.

College of Staten Island: Using R for Introductory Statistics : John Verzani: link or download it here.

SimpleR is a previous version of John Verzani's ebook. Also Table of Useful R commands, Calvin College.

Getting Started with Minitab 17 (PDF) by Minitab.

Probability Distributions in R, University of Minnessota.

My R notes: manage_data, anova_1, anova_2: (MS Word)

UMassAmherst: Basic logic ebook online pdf.
Math.northwestern.edu: Logic proofs, by A.J. Hildebrand
Truth Table generator by L. E. Turner PhD.

Differential Equations resources:

Diff Eqns: The Pennsylvania State University, Prof Tseng.
MIT opencourseware: Professor Arthur Mattuck at MIT.
Diff Eqns: Univsersity of Canterbury.
Professor Voutsadakis: site & slides, ode(zip).
Houston Math Prep: youtube channel
ODE-Summary, by integral-table.com

Diff Eqns Solver

Physics Videos by Eugene Khutoryansky