Acknowledgements
Surfaces are a special class of topological spaces that crop up in many places in the world of mathematics. In this unit, you will learn to classify surfaces and will be introduced to such concepts as homeomorphism, orientability, the Euler characteristic and the Classification Theorum.
Learning outcomes
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Learning outcomes
You may have met complex numbers before, but not had experience in manipulating them. This unit gives an accessible introduction to complex numbers, which are very important in science and technology, as well as mathematics. The unit includes definitions, concepts and techniques which will be very helpful and interesting to a wide variety of people with a reasonable background in algebra and trigonometry.
An analysis of learner arguments in a collective
This contribution analyses the arguments of students in a learning activity entitled "Argue Graph".
This activity is intended to make students understand the relationship between learning theories and design
choices in courseware development. The analysis of arguments is centered on the effects of discussion and
opinion conflict on the elaboration of arguments. We then use an adaptation of a collective intelligence model
to describe the knowledge flow among people and artifacts during the learni
Pupil groupings within classrooms: social pedagogy within cultural contexts
There have been many studies of teaching and learning in classrooms, for example, involving teaching approaches and styles, learning or broad classroom level structures (e.g. age of pupils, ability, curriculum). These studies offer insights into teaching effectiveness, patterns of learning and broad explanations of classroom effects, yet they add little insight into the complex ecology that characterises children’s development in school contexts. Studies of teaching and learning within classro
The restless Universe
The restless Universe introduces you to major achievements and figures in the history of physics, from Copernicus to Einstein and beyond. The route from classical to quantum physics will be laid out for you without recourse to challenging mathematics but with the fundamental features of theories and discoveries described in sufficient detail to whet your appetite for further physics study.
Math in Society
Math in Society is a free, open textbook. This book is a survey of mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriat
Can I Divide This Number By That Number?
Divisibility Rules presented in an easy-to-understand slideshow. (28 slides)
Mathematical divisibility rules; correlates with Glencoe Mathematics Course 1: 1-2 and Pre-Algebra: 4-1.
Derivatives in Physical Science The function of mathematics in physical science. From a theoretical concept to a practical tool, the derivative helps to determine the instantaneous speed and acceleration of a falling body. Differentiation is developed further to calculate how any quantity changes in relation to another. The power rule, the product rule, the chain rule -- with a few simple rules, differentiating any
Looking at Learning ... Again, Part 2: Workshop 2. Mathematics: A Community Focus
With Dr. Marta Civil. As teachers, we often make assumptions about the knowledge children are exposed to at home. Sometimes it seems that we focus on only reading and writing,Dr. Civil contends that we need to look more carefully at the mathematical potential of the home and that it is essential that schools learn to be more flexible and knowledgeable about studentsÂ’ home environments. See and hear from Dr. Civil, the teachers she works with, and a long-standing parent mathematics group, and fo
1.9 Distance between points in three-dimensional Euclidean space
Attempts to answer problems in areas as diverse as science, technology and economics involve solving simultaneous linear equations. In this unit we look at some of the equations that represent points, lines and planes in mathematics. We explore concepts such as Euclidean space, vectors, dot products and conics.
Uniform convergence and pointwise convergence
The aim of this material is to introduce the student to two notions of convergence for sequences of real-valued functions. The notion of pointwise convergence is relatively straightforward, but the notion of uniform convergence is more subtle. Uniform convergence is explained in terms of closed function balls and the new notion of sets absorbing sequences.
The differences between the two types of convergence are illustrated with several examples. Some standard facts are also discussed: a unif
Science In Focus: Energy
Interview with Dr. Sallie Baliunas about forms of energy including springs and magnets.,Dr. Sallie Baliunas explains the energy transfers that occur when she pushes down on a spring and then releases it. She explains that she adds potential energy to the spring when she pushes it down, energy that is bound up in the coils. When she releases the spring, the potential energy becomes energy of motion. Some potential energy is used to move air molecules, producing sound, and some is lost to heat
Vectors
Vectors: mathematics 1, level 4, is a presentation about Vectors for level 4 Mathematics and forms part of the 2009/2010 Engineering (foundation degree, BEng and HN) courses from University of Wales Newport (course codes H101, H691, H620, HH37 and 001H). It is a part of the core modules for the full time 1st year undergraduate programme.
This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The pro
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
TALAT Lecture 3205: The Fluidity of Molten Metals
This lecture introduces the concept of fluidity of molten metal and its influence on the production of castings. The students will understand the relevance of fluidity, the means by which this is measured and the effect of alloy type. Basic understanding of foundry processes, phase diagrams, basic physics and mathematics background is assumed
Mathematics I
A first course in Mathematics for Physics students. Contains lecture notes, examples, ... as well as the files used to create these resources. Discusses: 1-Vectors in 2-space and 3-space; 2-Differentiation; 3- Integration; 4- Applications of Integration and 5- Differential Equations.
18.303 Linear Partial Differential Equations (MIT)
This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.
RIAlity
The package was written in 1996. Radio immuno assay (RIA) is a technique for measuring concentrations of antigens. Although better techniques have subsequently been developed from it, understanding RIA forms the basis for understanding these derivatives. RIA belongs to the family of competition assays which are widely used in science, medicine and related industries to measure the concentrations of biologically active molecules. This package introduces the concepts of RIA and will be useful to a
Mathematics for Chemistry Videos
Videos illustrating solutions to problem topic in the context of mathematics skills for undergraduate chemistry students
