AdvancedMathematics.docx
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1、Advanced MathematicsAdvanced Mathematics The content of advanced mathematics from: advanced mathematics than elementary mathematics advanced mathematics. Broadly speaking, outside of elementary mathematics mathematics are advanced mathematics, also have high school will be deeply algebra and geometr
2、y and simple set theory logic called secondary mathematics, as a primary school junior high school of elementary mathematics and undergraduate course phase of the advanced mathematics the transition. Often think, advanced mathematics is will simply calculus, probability theory and mathematical stati
3、stics, and in-depth algebra and geometry, as well as their cross between formed a basic subject, mainly including calculus, other aspect of slightly different textbooks As with the development of basic concepts, the need for concrete experiences is critical to the development of many advanced mathem
4、atical concepts for a student who is blind. Acting out story problems and applying these problems to everyday situations is just as important at the advanced levels of mathematics as it is at basic levels, if students are to become capable of using their mathematics skills in functional situations o
5、r as a foundation in their pursuit of even more advanced mathematical and scientific learning. The use of models, manipulatives, and real life items found in everyday classrooms and living environments also plays an important role in providing support to the development of mathematical skills and co
6、ncepts at all levels. These items can be used for functional measuring, comparing, deduction and induction, as well as for motivating students to solve relevant problems. The following strategies are intended as illustrative examples of the use of concrete experiences to support higher mathematics c
7、oncepts. They are included here as representative samples only; teachers are encouraged to develop an array of concrete experiences and problem-solving situations to help students understand the concepts involved in higher mathematics. Course objectives: This course is designed to assist in the tran
8、sition from computation-oriented mathematics to the proof-based framework of most of advanced mathematics. We will begin with the study of propositional logic via truth tables, and proceed to the set theory that most working mathematicians need to know in their daily work. Topics will include functi
9、ons and relations, infinite cardinal and ordinal numbers, uncountability, transfinite arithmetic, the Axiom of Choice and Zorns Lemma. Emphasis in this course will be on learning to write clear proofs. Program Description A four-year degree leading to the potential award of honours based on overall
10、performance. The degree will incorporate a single major and a research project. The degree program divides into four groups covering discipline-specific technical content, research project, free electives and the general education components. Whereas the development of depth of understanding in pure
11、 and applied areas of mathematics and practical skills in specific disciplines are essential, the degree will also focus on instilling a culture of research and enquiry through early induction into the research ethos and access to research groups and facilities. Program Objectives and Graduate Attri
12、butes This program has been designed to: 1. Graduate Mathematicians and Statisticians with both breadth and depth of mathematics, statistics and scientific knowledge and professional skills; Develop the capacity for critical thinking and independent learning; Provide training in the practice and man
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