Mathematical analysis

This is a module framework. It can be viewed online or downloaded as a zip file.
As taught in 2007-2008 and 2009-2010.
This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration.
A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing t

Mathematical language

In our everyday lives we use we use language to develop ideas and to communicate them to other people. In this unit we examine ways in which language is adapted to express mathematical ideas.

8.7 Distance-time graphs: a mathematical story

Graphs are a common way of presenting information. However, like any other type of representation, graphs rely on shared understandings of symbols and styles to convey meaning. Also, graphs are normally drawn specifically with the intention of presenting information in a particularly favourable or unfavourable light, to convince you of an argument or to influence your decisions.

Why do we do proofs?

The aim of this session is to motivate students to understand why we might want to do proofs, why proofs are important, and how they can help us. In particular, the student will learn the following: proofs can help you to really see WHY a result is true; problems that are easy to state can be hard to solve (Fermat's Last Theorem); sometimes statements which appear to be intuitively obvious may turn out to be false (the Hospitals paradox); the answer to a question will often depend crucially on t

The Language of Mathematics (28): Proofs Involving a Line, Part 2

Clear, straightforward instruction involving how to solve proofs. Instructor uses a small chalkboard for demonstration.

Applied Mathematical Economics

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A Problem Course in Mathematical Logic

A Problem Course in Mathematical Logic is intended to serve as the text for an introduction to mathematical logic for undergraduates with some mathematical sophistication. It supplies definitions, statements of results, and problems, along with some explanations, examples, and hints. The idea is for the students, individually or in groups, to learn the material by solving the problems and proving the results for themselves. The book should do as the text for a course taught using the modified Mo

Logic & Proofs

This is an introductory course designed for students from a broad range of disciplines, from mathematics and computer science to drama and creative writing. The highly interactive presentation makes it possible for any student to master the material. Concise multimedia lectures introduce each chapter; they discuss, in detail, the central notions and techniques presented in the text, but also articulate and motivate the learning objectives for each chapter.
Topics Covered: The notions of statem

Mathematical Methods of Engineering Analysis

Mathematical Methods of Engineering Analysis

Children Play - The Foundation for Mathematical Learning

Children acquire mathematical concepts from games such as rope, dice and cards. This book identifies the games as a foundation for mathematical learning in Grades 1 to 3.

How and why we do mathematical proofs

This is a module framework. It can be viewed online or downloaded as a zip file.
As taught in Autumn Semester 2009/10
The aim of this short unit is to motivate students to understand why we might want to do proofs (why proofs are important and how they can help us) and to help students with some of the relatively routine aspects of doing proofs.
In particular, the student will learn the following:
* proofs can help you to really see why a result is true;
* problems that are easy to state

Mathematical Biology

These are my lecture notes for a course I teach on mathematical biology at the Hong Kong University of Science & Technology. My main emphasis is on mathematical modeling, with biology the sole application area.

Mathematical analysis

This is a module framework. It can be viewed online or downloaded as a zip file.
It is as taught in 2009-2010.
This module introduces mathematical analysis building upon the experience of limits of sequences and properties of real numbers and on calculus. It includes limits and continuity of functions between Euclidean spaces, differentiation and integration.
A variety of very important new concepts are introduced by investigating the properties of numerous examples, and developing the assoc

Professorial Lecture: Professor Bob Hale - The Problem of Mathematical Objects - a Modest and Sober

Professorial Lecture: Professor Bob Hale - The Problem of Mathematical Objects - a Modest and Sober Platonism

18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathemati

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

Author(s):

4 Proofs in group theory

We all encounter symmetry in our everyday lives, in both natural and man-made structures. The mathematical concepts surrounding symmetry can be a bit more difficult to grasp. This unit explains such concepts as direct and indirect symmetries, Cayley tables and groups through exercises, audio and video.

1.2 A Babylonian mathematical problem

This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.

1.7 Babylonian mathematical style

This unit looks at Babylonian mathematics. You will learn how a series of discoveries have enabled historians to decipher stone tablets and study the various techniques the Babylonians used for problem-solving and teaching. The Babylonian problem-solving skills have been described as remarkable and scribes of the time received a trainng far in advance of anything available in medieval Christian Europe 3000 years later.

1.7: Some mathematical themes

This unit looks at a wide variety of ways of comparing prices and the construction of a price index. You will also look at the Retail Price Index (RPI) and the Consumer Price Index (CPI), indices used by the UK Government to calculate the percentage by which prices in general have risen over any given period. You wil also look at the important statistical and mathematical ideas that contribute to the construction of a price index.

A mathematical muse

This unit explores reasons for studying mathematics, practical applications of mathematical ideas and aims to help you to recognise mathematics when you come across it. It introduces the you to the graphics calculator, and takes you through a series of exercises from the Calculator Book, Tapping into Mathematics With the TI-83 Graphics Calculator. The unit ends by asking you to reflect on the process of studying mathematics. In order to complete this unit you will need to have obtained a Texas I