AdvancedMathematics.docx

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 geometry 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 statistics, 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 mathematical 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 or 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 concepts 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 concepts. 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 transition 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 functions and relations, infinite cardinal and ordinal numbers, uncountability, transfinite arithmetic, the Axiom of Choice and Zorn's 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 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 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 Attributes 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 management of research and instill a research ethos; 4. 5. Endue general and science-specific graduate attributes; Expose students to disciplines outside mathematics and science, and the social context of science. 2. 3. Program Structure When completing the Bachelor of Science (Advanced Mathematics) as a single degree, students must complete a minimum of 192 units of credit. This 192 units of credit is comprised of: TOTAL OF 192 UOC 144 UOC * An approved Bachelor of Science (Advanced Mathematics) major; and * SCIF1121 or SCIF1131; * 48 units of credit Honours Year; and * Science elective courses 1 ('Science' courses are defined in Table 1 below.) 36 UOC 12 UOC * Free electives1: these courses can be taken from any Faculty of the university. * General Education courses: these courses cannot be Science courses. 1. Note: The Quantitative Risk major is a large multi-disciplinary major which is comprised of 114 units of credit. The Quantitative Risk major (114 UOC) plus SCIF1121/1131 (6 UOC) plus Honours (48 UOC) is a total of 168 UOC. Therefore students nominating to take a major in Quantitative Risk will not be required to take any additional science courses, and will only have 12 units of credit of free electives available. Where a student studies the Bachelor of Science (Advanced Mathematics) concurrently with another UNSW undergraduate degree program, they are required to complete a minimum of 144 units of credit comprised of an approved Bachelor of Science (Advanced Mathematics) major, SCIF1121/1131, Honours, and science elective courses, ie. the blue coloured area in the table above. Single Degree Program Rules Academic rules relating to the Bachelor of Science (Advanced Mathematics) are as follows: 1. Students in the single degree program must complete a minimum of 192 units of credit. 2. Students must complete exactly one approved Bachelor of Science (Advanced Mathematics) major, and this must be declared before enrolling in level III courses. Students cannot undertake a double major in this program. Information on how to declare a major can be found on the Science Student Centre website. 3. Approved majors in the Bachelor of Science (Advanced Mathematics) program are: · · Applied Mathematics; · High Performance Student Plan; Pure Mathematics; Quantitative Risk*; Advanced Statistics. · · *Enrolment in the Quantitative Risk major requires permission from the Head of School of Mathematics and Statistics. 4. SCIF1121 Advanced Science: Professional Perspective and Practice (6 units of credit) or SCIF1131 Science: Technological and Professional Perspectives (6 units of credit) must be completed in first year. 5. An Honours Year of 48 units of credit must be completed. For information regarding the admission requirements and application process for honours, please see the information below under 'Honours'. 6. In addition to the courses required for a student's chosen major, SCIF1121/1131, and honours, students must take 'science' courses so that the major plus SCIF1121/1131, plus Honours year plus 'science' courses total 144 units of credit. Majors in the Bachelor of Science (Advanced Mathematics) range from 84 units of credit to 114 units of credit. Honours is 48 units of credit, and SCIF1121/1131 is 6 units of credit, therefore students will typically need to take 0 - 6 units of credit of additional 'science' courses. This additional science course may need to be at level I depending on whether a major satisfies rule 7 below. 'Science' courses are courses offered by the following Schools. The course prefixes that are associated with each School are in bold below: