Linear transformations Multiplication by a 2x2 matrix can be used to transform points in the x-y plane — such tranformations are called linear since they map straight lines to straight lines. See what happens to the kiwi for each of these matrices. (Move the cursor over each matrix.)     Which of these do you think is reversible? Sample problem After an evening’s competition the six couples from the “Twirling Dervishes” Ballroom Dancing team headed off to the local pub for a drink. A fairly simple tavern, their local offers six different beers and four types of wine. Having crammed themselves around a table their captain, Fred, volunteered to get in the first round. Armed with the numbers of each type of drink required he set off for the bar. Being a bit of a wag, Fred decided to perform a pirouette on the way and became dizzy. When he reached the bar he had completely forgotten the order. Too embarrased to go back and ask for the order again, he just made up a selection of twelve drinks from those on offer. What is the probability that he got the order right? 
Arthur Cayley, 1821-1895, published over 900 papers and notes covering nearly every aspect of modern mathematics. The most important of his work was in developing the algebra of matrices, work in non-euclidean geometry and n-dimensional geometry. |
MATH103 Supplementary Algebra 2First Semester, Second Semester, 9 points Paper detailsThis paper first expands on the material on vectors and matrices begun in MATH 160/101. (Note, however, that sufficient background is provided on these topics to enable MATH 170 to be taken directly from school.) The course goes on to consider the determinant (a number associated with a matrix) and linear transformations (special mappings associated with computer graphics). The final section considers numbers and factorization, induction (used to prove sequential statements involving integers) and various counting techniques.Potential studentsMATH 103 is taken only by students who need the algebra component (but not the calculus) of MATH 170. This situation may arise when a student has transferred from another university, or has previously taken the calculus half.Main topics
PrerequisitesMATH 160 or MATH 101 or high achievement (mostly Excellences and Merits) in NCEA Level 3 Mathematics with CalculusRequired textMATH 170 Algebra Outline Notes(Available from the Print Shop.) Useful referencesSeveral standard texts are suitable for reference. For example:Elementary Vector Algebra by A.M. MacBeath Algebra, Geometry and Trigonometry by M.V. Sweet Elementary Linear Algebra (Applications version) by H. Anton and C. Rorres (7th edition) Introductory Linear Algebra (with applications) by B. Kolman (6th edition) Lecturer1st semester: Dr John Shanks (Room 221)2nd semester: Prof Robert Aldred (Room 233) LecturesAlgebra: approximately 25 lectures, Tuesday and Thursday at 12 noonTutorialsAttendance at tutorials is voluntary. An open system operates: tutorial classes run for up to 10 hours per week (depending on demand), and students may attend as many as they need to and are able to.Internal AssessmentFive computer Skills Tests make up 20% of your final mark. The other 80% comes from a mix of your final exam mark and the internal assessment mark which is based solely on the ten marked weekly assignments.Each week, several problems will be marked with an asterisk (*), and it is important to realize that although your solutions to all these “starred” problems are to be handed in, only a selection of them may be marked. You can check your marks by clicking on the Resources link at the top of this page. Terms RequirementYou have to fulfil the terms requirement in order to be allowed to sit the final exam. In this paper, to pass “terms” you need to gain at least 6/10 in each of the first four Skills Tests.Exam formatThe 90-minute final exam is answered in spaces provided on the question booklet. All questions should be attempted and the number of marks available for each question is indicated on the paper. There are usually about 12 to 15 questions.Final markThe final mark F is calculated from:F = max { E, (4E + A)/5 } + T where E (exam mark) is out of 80, A (internal assessment) is out of 80, T (test mark) is out of 20.The “max” corresponds to plussage: if your internal assessment mark is greater than your exam mark then it is combined in the proportion shown. If it is less then it is ignored and the exam mark itself is used. So your internal assessment counts at 1/5 weighting if that helps you. PlagiarismStudents should make sure that all submitted work is their own. “Plagiarism is a form of dishonest practice. Plagiarism is defined as copying or paraphrasing another’s work and presenting it as one’s own” (University of Otago Calendar). In practice this means that plagiarism includes any attempt in any piece of submitted work (e.g. an assignment or test) to present as one’s own work the work of another (whether of another student or a published authority). Any student found to be responsible for plagiarism in any piece of work submitted for assessment shall be subject to the University’s dishonest practice regulations which may result in various penalties, including forfeiture of marks for the piece of work submitted, a zero grade for the paper, or in extreme cases exclusion from the University. The University of Otago reserves the right to use plagiarism detection tools.
While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.
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