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MIT MATH 52 - Study Guide

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MA 52, Section 1Course Goals & GradingMath 52, Spring 2006You will study the following topics:This list is subject to slight change as the course evolves.• solutions of systems of linear equations• matrices and matrix operations• solving matrix equations• linear transformations• the geometry of Rn• vector spaces; basis, dimension, linear independence, subspace• norms, dot products, geometry of vector spaces• orthogonality and least squares• Gram-Schmidt process• Determinants• eigenvalues and eigenvectors• applicationsYou will develop the following skills for interacting with and using this knowl-edge:• writing of mathematics and the expression of clear thinking• logical reasoning using the concepts of hypotheses, conclusions and definitions• solving problems using established methods• developing appropriate problem solving methods• translating applications into mathematical problems to be solvedMA 52, Section 1You will be graded on your knowledge of the topics through the use of theseskills. The basic methods of evaluation are the posing of problems to which solutionsmust be submitted in written form. These take the forms of timed exams and deadlinedhomeworks.Grading: Your grade depends on you: there will be no surprises, if you read and understandthe following criteria.Criteria for a pass (letter grade of C) The student. . .• has habitual (but not necessarily perfect) accuracy in calculations• has ability to apply basic methods to standard problems• does not make false statements in the write-up of solutions• has knowledge of key definitions and theorems, and the ability to recognize situ-ations in which they applyCriteria for a letter grade of B In addition to the above, the student. . .• has the ability to make simple deductions based on key definitions and theorems• shows all the steps in calculation and justifies his/her methods• has the ability to adapt to small changes in problems (as compared to examplescovered in class) by adapting the methods appropriately• has the ability to recognize a new situation in which known methods apply• writes generally neat and organized solutionsCriteria for a letter grade of A In addition to the above, the student. . .• has the ability to reason new abstract deductions using definitions and theorems• has the ability to create new solutions to new problems using established concepts• has the ability to explain his/her reasoning in a clear and concise manner• always writes neat, organized, and detailed solutionsHow to get the grade you want:As you work on this course, you should pay attention to developing the general skillsof visual intuition, comfort with abstract ideas, problem solving skills, and writing skills.These general skills will help you reach the specific skills cited above, that determine yourgrade. These skills are all incredibly relevant to “the rest of your life”, and are one of themost valuable things you can take from this course.Since these skills are subtle and abstract, the best advice is to study examples and worksolutions with a consciousness of these things in mind. By asking yourself as you read, “whatMA 52, Section 1makes this a well-written logical argument?” or stopping to practice visualizing a problemwhenever it involves lines and planes, you will gradually develop these. The coursework,lectures and text, are all designed to give you a chance to develop these skills throughworking with the material of linear algebra. I will do my best to practice these habits aloudin class during lecture, and you should do your best to practice them at home.Here are some specific suggestions:• Read critically and actively. Ask “why?” frequently. When the text refers to a previousdefinition or fact, go back and look it up. Read and follow the guidelines in the handout“How to Read Your Textbook” available on the course website.• Approach problems with lots of questions. When a problem concerns the applicationof a theorem, stop to ask yourself, “what are the hypotheses?” and check that eachis satisfied one-by-one. For every problem you address, stop to ask, “What otherproblems does this remind me of? How is it the same? How is it different? What partof the solutions I already know will apply to this?” Read and follow the guidelines inthe handout “How to Do Your Homework” available on the course website.• Visit the course website for additional resources. An online recommendation is that of the types of problems listed under “Problem Solving” as 1–5, we areexpected to tackle all five in this class.) For something more in depth, try G. Polya’sbook How to Solve

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