2018-01-12.ipynb

Kernel: Python 2 (SageMath)

Math 157: Intro to Mathematical Software

UC San Diego, winter 2018; materials by Kiran S. Kedlaya

Homework 0 (practice): due January 12, 2018

This homework is not for credit. Its primary purpose is to give you a chance to practice with CoCalc, Jupyter notebooks, and the homework submission mechanism. A secondary purpose is to collect some feedback which might help us later.

In general, each homework will be presented as a single Jupyter notebook like this one. Each component of each problem will be followed by an empty cell in which you should provide your response (unless otherwise instructed). Please set the type of that cell appropriately: to "code" for executable code in some software package (the default), "markdown" for text wth formatting, or "raw" for text without formatting (we won't use this option much).

Problem 1: Background

1a. Please list (by name and course number) any programming classes you have taken.

1b. Are you familiar with any programming languages? If so, which ones?

1c. Have you used any mathematical software before (e.g., Mathematica, Maple, Matlab)? If so, in what way(s)?

1d. Feel free to make any more comments about your programming/math software background here, so we may better serve you.

Problem 2: Office hours

Are you able to attend any of the scheduled office hours? (If you are unable to utilize your TA's office hours, you may use another other TA's office hours.)

Problem 3: Paradigms for mathematical software

Most problem sets will include one or two verbal response questions in the following style.

3a. In your own words, explain the differences between the following concepts:

• a programming language (e.g., Python);

• a computer algebra system (e.g., Mathematica);

• a collaborative mathematics environment (e.g., CoCalc).

3b. WolframAlpha is a web service based on Mathematica, but it is a "computational knowledge engine" rather than a "collaborative mathematics environment". Explain the difference between these two concepts by giving some examples (on both sides) of tasks that can be handled by one type of web service but not the other.

Problem 4: Markdown syntax

Write some text in Markdown that illustrates at least three formatting features not used anywhere in this homework. Your text should also describe in words what these features are. (Do not use any examples based on TeX; that is, do not use the dollar sign $ in your text.)

Problem 5: TeX syntax

For Jupyter notebooks in CoCalc, markdown cells can contain mathematical formatting using TeX. Any text enclosed between a pair of dollar signs is parsed as TeX, for instance, $x^2$.

Use TeX to typeset the following equations/formulas:

• Euler's identity (according to Wikipedia);

• Stirling's approximation (the "more precise variant" according to Wikipedia);

• Laplace's equation (the first form appearing in Wikipedia).