Mathematics Articles

General Mathematics

Math Sites and Software (revised Sep 5, 2007)
Help desks, FAQs, Web-based software, and more

TI-83/84 Troubleshooting (revised Dec 7, 2008)
Got a screen full of lines? the “INVALID DIM” message? Lost a list?

Significant Digits and Rounding (revised Jan 31, 2007)

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 Jul 8, 2004)

Combining Operations (Distributive Laws) (revised Apr 20, 2004)

Solving Polynomial Equations (revised Sep 12, 2008)

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 Sep 30, 2007)

Quadratic Equations on the TI-83/84 (revised Aug 5, 2007)
with TI-83/84 program QUADRAT for download

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

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

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

Drawing Inverse Functions on the TI-83/84 (revised Aug 5, 2007)

Complex Numbers on the 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 the TI-83/84 (revised Aug 7, 2007)
with TI-83/84 program VECADD for download

Multiplying Vectors on the 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

Descriptive Statistics Utilities for the TI-83/84 (revised Dec 13, 2008) includes some utilities for probability
with TI-83/84 program MATH200D 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 the TI-89 (revised Aug 7, 2007)

Trigonometry

Trig without Tears (revised Jun 4, 2008)
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 the TI-83/84 (revised Dec 8, 2008)
mean, median, standard deviation, five-number summary, and more

Descriptive Statistics Utilities for the TI-83/84 (revised Dec 13, 2008)
histograms, frequency polygons, time-series graphs, skewness and kurtosis, binomial probability, check for normality, and more
with TI-83/84 program MATH200D for download

Measures of Shape: Skewness and Kurtosis (revised Dec 13, 2008)

Least Squares, Down and Dirty (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 the TI-83/84 (revised Sep 20, 2008) or on the TI-89

Decision Points for Correlation Coefficient (revised Sep 23, 2007)

Getting ŷ from Any x in a Regression on the TI-83/84/89 (revised Aug 7, 2007)

Statistics, Inferential

Normal Calculations on the TI-83/84 or TI-89 (revised Mar 25, 2008)
in a normal distribution, finding probability or inverse probability

Triage: Which Inferential Stats Case Should I Use? (revised Apr 26, 2008)

Inferential Statistics Cases (revised Sep 9, 2008)
a summary of inferential statistics from a first course in stats

How Big a Sample Do I Need? (revised Nov 11, 2008)

Top 10 Mistakes of Hypothesis Tests (revised Jul 4, 2008)

Inferential Statistics Utilities for the TI-83/84 (revised Dec 7, 2008)
estimate sample size; confidence intervals and hypothesis tests for standard deviation, correlation, and regression; critical t and chi-squared
with TI-83/84 program MATH200I for download

Inferences about One Population Standard Deviation (revised Nov 24, 2008)

List Operations for Paired t Test on the TI-83/84 (revised Oct 28, 2007)
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 Apr 4, 2008) explains how to tell whether there is correlation in the population, and how strong it is

Inferences about Linear Regression (revised Apr 4, 2008) 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 the TI-89 (revised Jun 1, 2008)

Calculus

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

Derivatives on the TI-83/84 (revised Apr 29, 2006)

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

Newton’s Method on the 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 Jul 20, 2003)

u-Substitution — Changing Variables in Integrals (revised Jan 12, 2004)