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Results: 258 items
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Science, Maths & Technology

### Introduction to algebra

This free course is an introduction to algebra which builds on the idea of using letters to represent numbers. Section 1 looks at finding, simplifying and using formulas and includes useful tips on learning algebra. Section 2 introduces some of the terminology used in algebra and techniques such as evaluating and checking equivalence of expressions, identifying terms in an expression and collecting like terms. Section 3 looks at how to simplify terms and introduces index notation and multiplying powers. Section 4 looks at the use of brackets in algebra and section 5 covers solving, checking and using simple linear equations.

Free course
16 hrs
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Science, Maths & Technology

### Introduction to analysis

This free course is an introduction to analysis which looks at real numbers and their properties, with a particular emphasis on inequalities. Section 1 starts by revising rational numbers and their decimal representations. Then, real numbers are introduced as infinite decimals. Section 2 looks at rules for manipulating inequalities and finding the solution set of an inequality. Section 3 looks at various techniques for proving inequalities. Section 4 introduces the concept of a least upper bound. Section 5 looks at how least upper bounds can be used to define arithmetic operations on the set of real numbers.

Free course
16 hrs
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Science, Maths & Technology

### Second-order differential equations

This free course is concerned with second-order differential equations. Section 1 introduces some basic principles and terminology. Sections 2 and 3 give methods for finding the general solutions to one broad class of differential equations, that is, linear constant-coefficient second-order differential equations. Section 2 covers homogeneous equations and Section 3 covers inhomogeneous equations. Section 4 explains how extra information can be used to help to select particular solutions that are appropriate in given situations. Section 5 looks at the phenomenon of resonance to gain insights into the solutions of inhomogeneous linear constant-coefficient second-order differential equations.

Free course
16 hrs
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Science, Maths & Technology

### Dynamics

This free course is concerned with moving objects, that is, dynamics. Section 1 introduces concepts like position, velocity and acceleration, which describe the way an object moves. Section 2 discusses Newton’s laws of motion, which predict the motion of an object when the forces acting on it are known. Section 3 shows how Newton’s second law of motion can be used to predict the motion of objects. Section 4 concerns modelling some of the forces that occur in nature, which enables more realistic situations to be analysed. Section 5 looks at motion in more than one dimension.

Free course
16 hrs
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Science, Maths & Technology

### Medical statistics

This free course is concerned with some of the statistical methods used in epidemiology and more widely in medical statistics. Section 1 introduces cohort studies in which individuals are classified according to their exposure and followed forward in time to evaluate disease outcomes. Section 2 looks at models for cohort studies. Section 3 introduces case-control studies in which individuals are selected according to their disease status and past exposures are then ascertained. Section 4 covers testing for no association in cohort studies and case-control studies.

Free course
16 hrs
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Science, Maths & Technology

### Bayesian statistics

This free course is an introduction to Bayesian statistics. Section 1 discusses several ways of estimating probabilities. Section 2 reviews ideas of conditional probabilities and introduces Bayes’ theorem and its use in updating beliefs about a proposition, when data are observed, or information becomes available. Section 3 introduces the main ideas of the Bayesian inference process. The prior distribution summarises beliefs about the value of a parameter before data are observed. The likelihood function summarises information about a parameter contained in observed data and the posterior distribution represents what is known about a parameter after the data have been observed.

Free course
12 hrs
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Science, Maths & Technology

### Introduction to group theory

This free course is an introduction to group theory, one of the three main branches of pure mathematics. Section 1 looks at the set of symmetries of a two-dimensional figure which are then viewed as functions. Section 2 introduces an algebraic notation for recording symmetries and calculating composites and inverses of symmetries. Section 3 introduces definitions and looks at how to check axioms for a group. Section 4 looks at how to prove that some properties of groups already looked at are general properties shared by all groups. Section 5 extends the ideas of symmetry to three-dimensions.

Free course
16 hrs
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Science, Maths & Technology

### Introduction to linear equations and matrices

In this free course, matrices are used as a concise way of representing systems of linear equations which occur frequently in mathematics. Section 1 looks at simultaneous linear equations in two and three unknowns and then generalises the ideas to systems of linear equations. Section 2 develops a strategy for solving systems of linear equations. Section 3 looks at the algebra of matrices and shows that matrices can be thought of as a generalisation of vectors. Section 4 introduces the inverse of a matrix. Section 5 uses systems of linear equations to introduce the determinant of a square matrix.

Free course
16 hrs
Copyright: Stuart Miles at FreeDigitalPhotos.net
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Science, Maths & Technology

### Succeed with maths – Part 2

This free course, Succeed with maths Part 2, is a sequel to Part 1, in which you will continue to develop your mathematical knowledge and skills using everyday examples. The course takes a look at measurement of length, mass and volume, negative numbers and how to use these, scientific notation (based upon powers of 10), shapes and how to calculate their properties before finally turning to how to construct and read from tables, charts and graphs. It provides a solid foundation for you to continue with studies in any subject which requires some degree of mathematical knowledge.

Free course
24 hrs
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Science, Maths & Technology

### Introduction to differential equations

Differential equations are any equations that include derivatives and ----- in many situations. This free course, Introduction to differential equations, considers three types of first-order differential equations. Section 1 introduces equations that can be solved by direct integration and section 2 the method of separation of variables. Section 3 looks at applications of differential equations for solving real world problems. Section 4 introduces the integrating factor method for solving linear differential equations. The final two sections summ----- and revise the methods introduced in the previous sections and describe various other approaches to finding solutions of first-order differential equations and to understanding the behaviour of the solutions.

Free course
18 hrs
Copyright: Image courtesy of Stuart Miles at FreeDigitalPhotos.net
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Science, Maths & Technology

### Succeed with maths – Part 1

If you feel that maths is a mystery that you want to unravel then this free course is for you. It will guide you through how numbers are put together, give you confidence with using percentages, fractions and negative numbers and provide you with problem solving skills for your everyday life and the wider world.

Free course
24 hrs
Copyright: Used with permission
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Science, Maths & Technology

### Design thinking

Are you ever frustrated with something that you thought you could design better? This free course, Design thinking, will show you how to structure your natural creativity to come up with solutions to all kinds of problems, and have fun in the process too!

Free course
10 hrs
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