# Theory

AMB&S chap. 7, 8.

Goal:
Understanding the rational numbers, their algebra, and decimal represenatations. Recalling the basics of Euclidean geometry including Pythagoras' theorem, the geometric definitions of cos(v) and sin(v), and the fundamental formulas for cos(v+w) and sin(v+w).

Excercises:
7.1, 7.2, 7.4, 7.5a-d, 7.6, 7.7, 7.8a-c, 7.9ab, 7.10a-c, 7.11a-d, 7.13,
8.1, 8.2, 8.5.

# Matlab

Goal:
Learning to use Matlab as an elementary calculator, including variable assigments and list/vector operations such as .*, ./ and .^.
Learning to use the basic programming elements if, for and while in Matlab, to run code from script files, and some elementary graphics.

Topics:
+, -, *, /, ^, (), ., ans, variable assignments, who, whos, clear, redefinitions, lists/vectors, [], indexing, addressing components, :, linspace, list operations, .*, ./, .^, matrices, double indices, ,, ;, workspace, save load, quit.
fix, floor, ceil, round, format, eps, inf, NaN, script files, edit, if, elseif, else, end, ==, <, >, <=, >=, ~, &, |, for, while, return, text variables, eval, disp, search priority, path, mkdir, cd, pwd, documentation, type, help, plot, xlabel, ylabel, title, hold, subplot, grid.
Matlab Intro I Matlab Intro II Matlab Intro III

Project ideas:
Formulate mathematical models of rubber bands. Dig into the aritmetics of natural numbers. Leibschnitzels (discrete) way to understand integration. Is there a 3D Pythagoras' theorem? What is the length of a semi circle? Write a Matlab code that sorts a given vector v=[a b c], for example, given v=[3 4 1] the code changes v to v=[1 3 4]. Once you have a working code you may think of modifying it to make it shorter or more transparent, for example, and to generalize to vectors of arbitrary length.
Write a Matlab script that converts any given natural number p to binary form (like p=22 to p='10110').
Further project ideas.

/Kenneth