Mathematics Articles

General Mathematics

Math Sites and Software (revised Feb 16, 2009)
Help desks, FAQs, Web-based software, and more

TI-83/84 Troubleshooting (revised Jun 21, 2009)
Got a screen full of lines? the “INVALID DIM” message? Lost a list?

Significant Digits and Rounding (revised Mar 14, 2009)

Student Success

How to Succeed in Math (revised Sep 25, 2008)

Why is Math so Hard? (revised Jan 25, 2003)

How to Work a Math Problem (revised Sep 25, 2008)

Show Your Work! (revised Aug 19, 2005)

How to Study Math (revised Aug 15, 2006)

How to Take a Math Test (revised Jun 30, 2005)

How to Read a Math Book (revised Dec 18, 2004)

Math Students’ FAQ (revised Mar 5, 2003)

Algebra / Precalculus

How to Convert Units of Measurement (revised Feb 16, 2009)

Combining Operations (Distributive Laws) (revised Sep 13, 2009)

Factoring the Sum of Squares (revised Sep 13, 2009)

Solving Polynomial Equations (revised Sep 13, 2009)

It’s the Law — the Laws of Exponents (revised Feb 13, 2006)

It’s the Law Too — the Laws of Logarithms (revised Nov 13, 2008)

Loan or Investment Formulas (revised Aug 16, 2009)

Quadratic Equations on TI-83/84 (revised Nov 30, 2009)
with TI-83/84 program QUADRAT for download

Evaluating Functions with TI-83/84 (revised Aug 5, 2007)

Graphing Functions on TI-83/84 (revised Aug 5, 2007)
It’s easy to do, harder to do well.

Graphing Piecewise Functions on TI-83/84 (revised Oct 4, 2008)

Inverse Functions on TI-83/84 (revised Feb 15, 2009)

Complex Numbers on TI-83/84 (revised Aug 4, 2007) or on the TI-89
computations in polar form or rectangular form (a+bi)

Adding Vectors Graphically on TI-83/84 (revised Aug 7, 2007)
with TI-83/84 program VECADD for download

Multiplying Vectors on TI-83/84 (revised Sep 18, 2008)
with TI-83/84 program VECPRODS for download to compute scalar product (dot product) and vector product (cross product)

Probability

MATH200A Program — Statistics Utilities for TI-83/84 (revised Dec 28, 2009) includes some utilities for probability
with TI-83/84 program MATH200A for download

Probability of Shared Birthdays (revised May 25, 2003)
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 (revised Jan 12, 2004)

Binomial Probability Distribution on TI-89 (revised Aug 7, 2007)

Trigonometry

Trig without Tears (revised Aug 25, 2009)
You don’t need to memorize those identities!
(also available in a printer-friendly version)

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

Solving Trigonometric Equations (revised Feb 7, 2006)

Statistics, Descriptive

Sample Statistics on TI-83/84 (revised Dec 8, 2008)
mean, median, standard deviation, five-number summary, and more

MATH200A Program — Statistics Utilities for TI-83/84 (revised Dec 28, 2009)
histograms, frequency polygons, box-whisker diagrams, binomial probability, check for normality, and more
with TI-83/84 program MATH200A for download

MATH200B Program — Extra Statistics Utilities for TI-83/84 (revised Dec 28, 2009)
skewness and kurtosis, time-series graphs, and more
with TI-83/84 program MATH200B for download

Measures of Shape: Skewness and Kurtosis (revised Feb 11, 2009)

Least Squares — the Gory Details (revised Aug 9, 2007)
what we mean by the “line of best fit”, and how we find it — surprisingly, no calculus is required

Scatter Plot, Correlation, and Regression on TI-83/84 (revised Sep 22, 2009) or on the TI-89

Decision Points for Correlation Coefficient (revised Jun 10, 2009)

Getting ŷ from Any x in a Regression on TI-83/84/89 (revised Dec 30, 2009)

Statistics, Inferential

Normal Calculations on TI-83/84 or TI-89 (revised Aug 14, 2009)
in a normal distribution, finding probability or inverse probability

Triage: Which Inferential Stats Case Should I Use? (revised Jul 7, 2009)

Inferential Statistics Cases (revised Dec 26, 2009)
a summary of inferential statistics from a first course in stats

How Big a Sample Do I Need? (revised Aug 24, 2009)

Top 10 Mistakes of Hypothesis Tests (revised Aug 30, 2009)

MATH200A Program — Statistics Utilities for TI-83/84 (revised Dec 28, 2009)
estimate sample size; χ² goodness of fit
with TI-83/84 program MATH200A for download

MATH200B Program — Extra Statistics Utilities for TI-83/84 (revised Dec 28, 2009)
confidence intervals and hypothesis tests for standard deviation, correlation, and regression; critical t and chi-squared
with TI-83/84 program MATH200B for download

Inferences about One Population Standard Deviation (revised Dec 24, 2009)

List Operations for Paired t Test on TI-83/84 (revised Jul 26, 2009)
the calculator’s list operations make this a snap

Confidence Intervals for Two Populations (revised Jul 17, 2008)
estimating the mean difference for paired data, the difference in means for unpaired data, and the difference in proportions for binomial data

Case Study: Gardasil Vaccine (revised Oct 28, 2007)

Inferences about Linear Correlation (revised Dec 25, 2009) explains how to tell whether there is correlation in the population, and how strong it is

Inferences about Linear Regression (revised Dec 25, 2009) 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-89 (revised Jun 1, 2008)

One-Way ANOVA (revised Feb 3, 2009)

Calculus

The Derivative and the Tangent Line (revised Jun 8, 2005)
one of the big two problems of calculus

Derivatives on TI-83/84 (revised Dec 22, 2009)

Optimization (revised Jun 8, 2005)
maximum profit, minimum cost, and so forth

Newton’s Method on TI-83/84 or TI-89 (revised Jun 22, 2008)
with TI-83/84 program NEWTON for download to find solutions of an equation numerically

Area by Upper and Lower Sums (revised Jan 12, 2004)
introduction to integration

Definite Integrals on the TI-83/84 (revised Dec 22, 2009)

u-Substitution — Changing Variables in Integrals (revised Aug 15, 2009)