Under the topic of “Properties of integers”, we looked at various theorems and their formal proofs…

- Division algorithm
- Existance proof
- Uniqueness proof
- Eucledian algorithm
- Greatest common divisor

Under the topic of “Properties of integers”, we looked at various theorems and their formal proofs…

- Division algorithm
- Existance proof
- Uniqueness proof
- Eucledian algorithm
- Greatest common divisor

We continued into pair programming as an XP practice.

- The rule of pairing
- Benefits of pairing
- Some mistakes pairing fixes
- How to find your comfort zone when pairing

Yesterday, we did a brief revision of arc length (from Calculus II), and then its representation in vector-valued functions. Then we were off to how to change parameters of a function.

- Arc length
- Smooth parametrization
- Arc length of a parameter
- Change of parameter

We had a very interesting lecture on energy conservation yesterday using the Tour de France cyclists as an example of how energy losses and gains are balanced out!

Today we started a new topic on how computers can represent sets, and also how we can use regular expressions to define the syntax of a programming language.

- Computer representation of sets and subsets
- Countability of sets
- Strings and regular expressions
- Catenation

This day we finished up on an overview of basic XP practices, and moved into the details of one of them, pair programming. In pair programming, we discussed some advantages and disadvantages, and the roles of pair programmers:

- Driver
- Copilot

After concluding the BC phases of middle eastern history, we now get into the AD/ CE phases with Islamic civilizations. Today, we had an overview of the concept of Islam, and how it represents an entity comprised of…

- Culture/civilization
- Religion/faith
- State/nation

In our tutorials session, we started on the following topics…

- Parametrized curves
- Calculus of vector functions

Under the second topic, we are now revisiting limits, differentiation and integration from Calculus I and II, but this time with vector-value functions.

We had lectures today. Dr. Jeff Collier kindly came despite his recent illness. We had some solutions to difficult problems from the course text.

Yesterday we revised on polar coordinates before moving onto cylindrical and spherical coordinate systems. The evening class continued with a first look into Chapter 13, on vector-valued functions, strange functions that don’t return real numbers as results, but vectors instead! We closed by going over the finding the domain of vector-valued functions.