 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.

3Blue1Brown: Animated Math. NC State University:

Harvard Univ:

Math21a, Multivariable Calculus by Prof O. Knill.

Community Calculus: Whitman College, ebooks:

MULTIVARIABLE CALCULUS 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 Random:

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).

Casio FX-991EX
:
Instructions: descriptive stat.
Instructions: distributions.  OpenIntroOrg Stat using Graphing Calculators

fx-115 ES Plus: youtube video, min 40: stat Casio CFX-9850 Plus and CFX-9750 Statistics

Casio FX-9750GII
Guide for Introductory Statistics
by David Diez, OpenIntro. Calculators: instructions.

Descriptive Statistics in TI 83 & 84.
Normal CDF in TI 83 & 84.
Descriptive Statistics and Normal CD in TI 36 pro.
Descriptive Statistics in TI 30 II.
Descriptive Statistics and Normal CD on Casiofx115ES.
TI-NSpire: descriptive statististics by Dr. L Schultz.
TI-NSpire: Normal distribution by Dr. L Schultz.
TI-83 & TI-84 Tips for Statistics by NapaValley.edu
Casio FX-9750GII Statistics by David Diez, OpenIntro. Logic: the structure of reason:

UMassAmherst: Basic logic ebook online pdf.
Math.northwestern.edu: Logic proofsby 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
ODE-Summary, by integral-table.com
Nonhomogeneous linear ...
By Stewart Calculus. Diff Eqns Solver Mathematics
Physics Videos by Eugene Khutoryansky

Online notes, resourses: algebra, calculus, differential equations, statistics

by Carlos Sotuyo. Math/Stat instructor at Miami Dade College & Broward College.
csotuyo@broward.edu or csotuyo@mdc.edu

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: Statistics:

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

Content.

Introductory Statistics, Vol 1: textbookequity.org

Introductory Statistics, Vol 2: textbookequity.org

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.

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

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

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

### 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. " ### Power analysis: Effect size formulas, by UCLA.Power Analysis in R by Quick R, by DataCamp.

Calculation of Beta (PWR=1-Beta), for a test on mean(population SD estaimated by large sample SD) sampling from normal population or when n is large --for a one sided test, replace z_alpha/2 by z_alpha: Image created using codecogs.com latex equation editor.

### Power analysis in R: http://www.statmethods.net/stats/power.html

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).

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.

The R Project for Statistical Computing
https://r-project.org

### Columbia Univ: Statistics, R Notes.

Basic Statistical Analysis Using R:
by T. Heeren & J.Milton,
Boston University.

Quick R by statmethods.net

MarinStatlectures.com: R tutorials

Table of Useful R commands,
Calvin College.

Probability Distributions in R,
University of Minnessota.

College of Staten Island: Using R for Introductory Statistics:
John Verzani: