Mathematics Articles

General Mathematics

Math Sites and Software (revised 7 Jan 2011)
Help desks, FAQs, Web-based software, and more

TI-83/84 Troubleshooting (revised 26 Dec 2012)
Got a screen full of lines? the “INVALID DIM” message? Lost a list?

Significant Digits and Rounding (revised 20 Dec 2010)

Student Success

How to Succeed in Math (revised 13 Feb 2011)

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

How to Work a Math Problem (revised 6 Dec 2011)

Show Your Work! (revised 27 Jan 2011)

How to Study Math (revised 15 Aug 2006)

How to Take a Math Test (revised 13 Feb 2011)

How to Read a Math Book (revised 6 Dec 2011)

Math Students’ FAQ (revised 26 Dec 2012)

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 21 Apr 2011)

Solving Polynomial Equations (revised Jan 3)

It’s the Law — the Laws of Exponents (revised 6 Mar 2011)

It’s the Law Too — the Laws of Logarithms (revised 6 Feb 2012)

Loan or Investment Formulas (revised Apr 1)

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

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

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

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

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

Complex Numbers on TI-83/84 (revised 26 Jan 2011) or on the TI-89
computations in polar form or rectangular form (a+bi)

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

Multiplying Vectors on TI-83/84 (revised 18 Sep 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 27 Nov 2012) includes some utilities for probability
with TI-83/84 program MATH200A for download

Probability of Shared Birthdays (revised 25 May 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 Feb 3)

Binomial Probability Distribution on TI-89 (revised 17 Sep 2011)

Trigonometry

Trig without Tears (revised 25 Jan 2012)
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, Descriptive

Sample Statistics on TI-83/84 (revised 31 Dec 2010)
mean, median, standard deviation, five-number summary, and more

MATH200A Program — Statistics Utilities for TI-83/84 (revised 27 Nov 2012)
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 2 Aug 2012)
skewness and kurtosis, time-series graphs, and more
with TI-83/84 program MATH200B for download

Measures of Shape: Skewness and Kurtosis (revised 26 Dec 2012)

Least Squares — the Gory Details (revised 9 Aug 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-83/84/89/92 (revised Feb 21)

Decision Points for Correlation Coefficient (revised Feb 21)

Finding ŷ from a Regression on TI-83/84/89/92 (revised 28 Sep 2011)

Statistics, Inferential

Normal Calculations on TI-83/84 or TI-89 (revised 23 Oct 2012)
in a normal population or a sampling distribution, finding probability or inverse probability

Inferential Statistics Cases (revised 1 Aug 2012)
a summary of inferential statistics from a first course in stats

Triage: Which Inferential Stats Case Should I Use? (revised 26 Dec 2012)

How Big a Sample Do I Need? (revised Jan 1)

Top 10 Mistakes of Hypothesis Tests (revised 18 Dec 2010)

MATH200A Program — Statistics Utilities for TI-83/84 (revised 27 Nov 2012)
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 2 Aug 2012)
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 8 Jul 2012)

List Operations for Paired t Test on TI-83/84 (revised 23 Dec 2011)
the calculator’s list operations make this a snap

Confidence Intervals for Two Populations (revised 22 Jul 2012)
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 26 Dec 2012)

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

Inferences about Linear Regression (revised 20 Dec 2010) 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 20 Dec 2010)

Confidence Intervals for Goodness of Fit (revised 11 Jun 2011)

One-Way ANOVA (revised Mar 9)

Calculus

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

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

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

Newton’s Method on TI-83/84 or TI-89 (revised 18 Jul 2012)
with TI-83/84 program NEWTON for download to find solutions of an equation numerically

Area by Upper and Lower Sums (revised 23 Jul 2012)
introduction to integration

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

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