# Math Fifty-one

#### and more, for freshmen and sophomores

As of July 2014, this page is no longer maintained, because I've graduated. Maybe it will be reincarnated at a different address in the future.
All class-specific material below are arranged in chronological order of the class. These were originally typed to supplement my sections, so they might not make perfect sense alone. Explanation of the star system:
* formulaic. Free points on the exam, no excuses for not being able to do this!
** needs some thinking. Concentrate on these questions.
*** needs a bright idea. Don't worry about these questions until you can master ** material.
**** beyond the syllabus (careful, this varies quarter by quarter).
I welcome improvements to the material below, as well as suggestions for new resources.

### General study tips:

General study advice from Joan Licata
Prof Schechter's on common errors in undergrad
My advice on how to make the best of homework
Jessica Purcell's advice for doing well in exams
Joan's tips for writing proofs

### Precalculus (Math 41)

*Graph transformations

### Differential Calculus (Math 41)

**A flow chart for evaluating limits
!Mean Girls: the limit does not exist!
!What not to do if you see a wild exponential function
**Related rates worksheet
Math 41 midterm II question classification

### Integral Calculus (Math 41)

***Integration of inverse functions (without integration by parts)
!The "Stand and Deliver" method of tabular integration by parts
!Some integrals are hard

### Linear Algebra (Math 51)

Jon Lee's notes for Math51 - many of my past students have found this useful!
*Instructions for RREF
*Finding basis of nullspace and columnspace
****Rotations in higher dimensions
**Changing between two non-standard coordinates
**Solutions to Winter 2009 midterm II q6bc and Spring 2009 midterm II q5bc: projections, change of coordinates, eigenvectors
**Solution to Winter 2010 midterm II q5: spectral theorem

### Multivariable Differential Calculus (Math 51)

****Three ways to use the squeeze theorem
****Limits and "division by zero"
**Solution to Winter 2010 Final q2b: finding points where tangent plane is parallel to a given plane

Other fun maths things:
A talk I gave at SUMO in 2010 about the art gallery problem
Page coded with help from 1, 2, 3, 4, 5, 6, 7 and Jon. Fonts from Google, background modified from Dezignus