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Mathematics Articles

by Stan Brown, Oak Road Systems

Contents: General  |  Student Success  |  Algebra/Precalc  |  Probability  |  Trig  |  Statistics  |  Calculus

Can’t find an article? Check our sister site, BrownMath.com.

General Mathematics

Math Sites and Software (revised Jul 19)
Help desks, FAQs, Web-based software, and more

TI-83/84 Troubleshooting (at BrownMath.com) calculator procedure
Got a screen full of lines? the “INVALID DIM” message? Lost a list?

What’s Different between TI-83 and TI-84? (at BrownMath.com) calculator procedure

Student Success

How to Succeed in Math (at BrownMath.com)

Why is Math so Hard? (at BrownMath.com)

How to Work a Math Problem (at BrownMath.com)

Show Your Work! (at BrownMath.com)

How to Study Math (at BrownMath.com)

How to Take a Math Test or Quiz (at BrownMath.com)

How to Read a Math Book (at BrownMath.com)

Math Students’ FAQ (at BrownMath.com)

Algebra / Precalculus

How to Convert Units of Measurement (revised 17 Feb 2009)

Combining Operations (Distributive Laws) (revised 10 Jun 2010)

Factoring the Sum of Squares (revised Jul 20)

Solving Polynomial Equations (revised 3 Jan 2013)

It’s the Law — the Laws of Exponents (revised 7 Mar 2011)

It’s the Law Too — the Laws of Logarithms (revised 3 Jul 2013)

Loan or Investment Formulas (revised Jul 19)

Quadratic Equations on TI-83/84 (at BrownMath.com)
with TI-83/84 program QUADRAT for download calculator procedure

Evaluating Functions with TI-83/84 (at BrownMath.com) calculator procedure

Graphing Functions on TI-83/84 (at BrownMath.com) calculator procedure
It’s easy to do, harder to do well.

Graphing Piecewise Functions on TI-83/84 (at BrownMath.com) calculator procedure

Inverse Functions on TI-83/84 (at BrownMath.com) calculator procedure

Complex Numbers on TI-83/84 (at BrownMath.com) or on the TI-89 calculator procedure
computations in polar form or rectangular form (a+bi)

Adding Vectors Graphically on TI-83/84 (at BrownMath.com)
with TI-83/84 program VECADD for download calculator procedure

Multiplying Vectors on TI-83/84 (at BrownMath.com)
with TI-83/84 program VECPRODS for download calculator procedure to compute scalar product (dot product) and vector product (cross product)

Probability

MATH200A Program — Statistics Utilities for TI-83/84 (at BrownMath.com) includes some utilities for probability
with TI-83/84 program MATH200A for download calculator procedure

Probability of Shared Birthdays (at BrownMath.com)
In a group of N people, how likely is it that two or more share a birthday? How big a group do you need before it’s more likely than not?

Medical False Positives and False Negatives (at BrownMath.com)

Binomial Probability Distribution on TI-89 (at BrownMath.com) or on the TI-83/84 calculator procedure

Trigonometry

Trig without Tears (revised 10 Aug 2014)
You don’t need to memorize those identities!
(also available in a printer-friendly version)

10-Minute Trig (revised 28 Mar 2006)
for those who just want a fast review

Solving Trigonometric Equations (revised 6 Jul 2010)

Statistics — Free Textbook

Stats without Tears is a full textbook, over 160,000 words, with practice exerises and full solutions.

Statistics, Descriptive

Sample Statistics on TI-83/84 (at BrownMath.com) calculator procedure
mean, median, standard deviation, five-number summary, and more

MATH200A Program — Statistics Utilities for TI-83/84 (at BrownMath.com)
histograms, frequency polygons, box-whisker diagrams, binomial probability, check for normality, and more
with TI-83/84 program MATH200A for download calculator procedure

Box-Whisker Plots on TI-89 (at BrownMath.com) or on the TI-83/84 (revised 18 Dec 2012) calculator procedure

MATH200B Program — Extra Statistics Utilities for TI-83/84 (at BrownMath.com)
skewness and kurtosis, time-series graphs, and more
with TI-83/84 program MATH200B for download calculator procedure

Measures of Shape: Skewness and Kurtosis (at BrownMath.com)

Least Squares — the Gory Details (at BrownMath.com)
what we mean by the “line of best fit”, and how we find it—surprisingly, no calculus is required

Scatterplot, Correlation, and Regression on TI-89 (at BrownMath.com) calculator procedure

Finding ŷ from a Regression on TI-89 (at BrownMath.com) calculator procedure

Normality Check and Finding Outliers in Excel (at BrownMath.com)

Normality Check on TI-83/84 (at BrownMath.com) calculator procedure

Normality Check on TI-89 (at BrownMath.com) calculator procedure

Statistics, Inferential

Normal Calculations on TI-83/84 or TI-89 (at BrownMath.com) calculator procedure
in a normal population or a sampling distribution, finding probability or inverse probability

Inferential Statistics Cases (at BrownMath.com)
a summary of inferential statistics from a first course in stats

Triage: Which Inferential Stats Case Should I Use? (at BrownMath.com)

How Big a Sample Do I Need? (at BrownMath.com)

Top 10 Mistakes of Hypothesis Tests (at BrownMath.com)

MATH200A Program — Statistics Utilities for TI-83/84 (at BrownMath.com) calculator procedure
estimate sample size; χ² goodness of fit
with TI-83/84 program MATH200A for download calculator procedure

MATH200B Program — Extra Statistics Utilities for TI-83/84 (at BrownMath.com) calculator procedure
confidence intervals and hypothesis tests for standard deviation, correlation, and regression; critical t and chi-squared
with TI-83/84 program MATH200B for download calculator procedure

Inferences about One Population Standard Deviation (at BrownMath.com)

List Operations for Paired t Test on TI-83/84 (at BrownMath.com) calculator procedure
the calculator’s list operations make this a snap

Inferences about Linear Correlation (at BrownMath.com) explains how to tell whether there is correlation in the population, and how strong it is

Inferences about Linear Regression (at BrownMath.com) to do hypothesis tests and confidence intervals on slope of the regression line and on y responses to particular x values

Testing Goodness of Fit on TI-83/84 (at BrownMath.com) calculator procedure

Testing Goodness of Fit on TI-89 (at BrownMath.com) calculator procedure

Confidence Intervals for Goodness of Fit (at BrownMath.com)

One-Way ANOVA (at BrownMath.com)

Calculus

Derivatives on TI-83/84 (at BrownMath.com) calculator procedure

Optimization (at BrownMath.com)
maximum profit, minimum cost, and so forth

Newton’s Method on TI-83/84 or TI-89 (at BrownMath.com)
with TI-83/84 program NEWTON for download calculator procedure to find solutions of an equation numerically

Area by Upper and Lower Sums (at BrownMath.com)
introduction to integration

Definite Integrals on TI-83/84 (at BrownMath.com) calculator procedure

u-Substitution — Changing Variables in Integrals (at BrownMath.com)

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