# Classroom Capsules and Notes

Capsules By Courses. We are organizing the capsules into courses, when possible using the same topics as are used in Course Communities. So far we have organized capsules for the following courses:

• One-Variable Calculus
• Sequences and Series
• Multivariable Calculus
• Ordinary Differential Equations
• Number Theory
• Probability

Select Browse, then select the course in which you are interested. You may select topics within that course.

Notes: Sequences and Series is part of One-Variable Calculus. We felt that since this topic had so many capsules associated with it, we wanted to introduce sub-topics. Also, the Number Theory collection of capsules does not correspond to a course in Course Communities, but has topics selected by the Editorial Board for Classroom Capsules and Notes.

New: The Mathematics of Planet Earth 2013 Collection is now available. These are articles published in the three journals of the MAA that are related to the Mathematics of Planet Earth 2013 theme.

## Featured Items

##### A New Method of Trisection

Another approach to trisecting any acute angle

##### Tennis with Markov

Using eigenvalues to solve problems in transition matrices of Markov Chains

##### Root Preserving Transformations of Polynomials

Is there a (non-trivial) linear transformation $$T$$ from $$P_n$$, the vector space of all polynomials of degree at most $$n$$, to $$P_n$$ such that for each $$p$$ in $$P_n$$ with a real or complex root, the polynomials $$p$$ and $$T( p)$$ have a common root?

##### Uncountable Fields Have Proper Uncountable Subfields

Does an uncountable field have any uncountable proper subfields? This paper shows the answer is "yes, always."

##### Proof without Words: The Substitution to Make a Rational Function of the Sine and Cosine

The picture illustrates the values of $$\sin \theta$$ and $$\cos \theta$$ in terms of $$z=\tan \theta/2$$, as used to symbolically antidifferentiate.

##### Linear Transformation of the Unit Circle in $$\Re^2$$

Analysis of images of unit circle under non-singular linear transformations $$T$$, $$I+T$$