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 Aug 5, 2007)
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 Aug 16, 2007)

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

How to Work a Math Problem (revised May 28, 2006)

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 Oct 15, 2006)

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

It’s the Law Too — the Laws of Logarithms (revised Aug 27, 2006)

Loan or Investment Formulas (revised Sep 30, 2007)

Quadratic Equations on the TI-83/84 (revised Aug 5, 2007)
with a downloadable TI-83/84 program

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 Aug 5, 2007)

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 a downloadable TI-83/84 program

Multiplying Vectors on the TI-83/84 (revised Aug 7, 2007)
scalar product (dot product) and vector product (cross product), with a downloadable TI-83/84 program

Probability

Probability Histograms on the TI-83/84 (revised Sep 9, 2007)
making a histogram from a discrete probability distribution

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-83/84 (revised Mar 25, 2008) or on the TI-89

Histogram of a Binomial PD on the TI-83/84 (revised Sep 9, 2007)

Trigonometry

Trig without Tears (revised Jun 13, 2006)
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

Descriptive Statistics of a Data Set on the TI-83/84 (revised Jan 27, 2008)
mean, median, standard deviation, five-number summary, and more

Skewness and Kurtosis on the TI-83/84 (revised Jan 26, 2008)
with a downloadable TI-83/84 program

Plotting Time Series on the TI-83/84 (revised Sep 15, 2007)

Histograms of Numeric Data on the TI-83/84 (revised Jan 20, 2008)

Frequency Polygons on the TI-83/84 (revised Jan 26, 2008)
with a downloadable TI-83/84 program

Normality Check on the TI-83/84 or TI-89 (revised Feb 4, 2008)
determining whether a set of measurements probably comes from a normal distribution, with a downloadable TI-83/84 program

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 9, 2007) 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 Apr 6, 2008)
a summary of inferential statistics from a first course in stats

How Big a Sample Do I Need? (revised Apr 26, 2008)

Top 10 Mistakes of Hypothesis Tests (revised Nov 6, 2007)

Critical t on the TI-83/84/89 (revised Jan 27, 2008)
finding critical values for the Student’s t distribution

Inferences about Standard Deviation of One Population (revised Oct 28, 2007)

Computing Critical χ² on the TI-83/84/89 (revised Jan 26, 2008)
with a downloadable TI-83/84 program

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 Oct 28, 2007)
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)
based on correlation of the sample, how to tell whether there is correlation in the population, and how strong it is

Inferences about Linear Regression (revised Apr 4, 2008)
tests and predictions on slope of the regression line and on y responses to particular x values

Testing Goodness of Fit on the TI-83/84 (revised Apr 26, 2008) or on the TI-89
how to do a χ² (Chi-squared) test for categorical data, with a downloadable TI-83/84 program

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 Aug 5, 2007)
how 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)