Introduction to analysis |
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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. Course learning outcomesAfter studying this course, you should be able to: find a rational and an irrational number between any two distinct real numberssolve inequalities by rearranging into simpler equivalent forms and solve inequalities involving modulus signsstate and use the Triangle Inequality and use the Binomial Theorem and mathematical induction to prove inequalities which involve an integer nuse the strategies introduced for determining least upper bounds and greatest lower boundsexplain how the least upper bound property is used to define arithmetical operations with real numbers and explain the meaning of rational powers. Enter courseFirst Published: 08/12/2017 Updated: 17/04/2018 |
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