 # Part 1: Math. Analysis

This is a module that helps students believe that they may not have to do a lot of equations with proofs. It is an extension of studies that were covered in the past year and those in analytical and computational foundations. This module helps students to learn about what is true, why, and, how you can know it is true. It will also cover how to do proofs overall. It is full of proofs that you will have to understand and that you will have to produce during the exams. However, this module will give you a few exceptional tricks that you should memorize instead of 100 proofs – which may turn out to be ineffective at all.

## Lecture 1

This is the first lecture on mathematical analysis. The module will cover definitions and theorems. It will also cover examples, how the theory is covered in the module and how the proofs apply in all the things. There will be annotated slides and videos and audios from these classes. Most of the work here is examinable, and those parts that aren’t included because they are interesting and worth knowing. There is also coverage of common errors that students need to avoid in future. There will be basic and critical notations. It will work with coordinates that will be real numbers.

## Lecture 2a: Math. Analysis – properties of the Euclidian norm

This is a continuation of the vector class. We are dealing with the elements of vector spaces. Column vectors take a lot of space when writing them. You will need the modular signs if you are working on complex numbers. You will learn how to visualize when you have more than three dimensions. You will have to go through other notes to understand how to deal with proofs for these parts. You will understand triangle inequity and homogeneity. It covers land as scale. If the concepts are negative, you will have to borrow from modular because you will never have negative length when calculating.

## Lecture 2b: Math. Analysis – open balls and closed balls

This is chapter two which covers the boundedness of subsets of Rd. It is a straightforward concept that will cover the different sets of Rd and understanding which sets share certain properties and which ones are great sets when looking ate continuous functions of certain sets. It will also cover more interest domains. You will understand the words that make it difficult for people to understand what these sets are all about. The difference in how these terms are used in different modules make it confusing to students. It is important to understand the definitions and the examples.

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