Summer School details
Sample problem The Bright’nWarm Greenhouse people are installing a new lighting system. To provide light and warmth to their plants through overhead lighting they must decide on how many incandescent bulbs and fluorescent tubes to use to achieve the effect they want. Each bulb gives off 4 units of heat and 6 units of light while each tube gives off 2 units of heat and 9 units of light. The bulbs cost $3.00 each and the tubes cost $4.00 each. The system must provide at least 20 units of heat and at least 54 units of light. How many bulbs and tubes should they use to minimize the cost? Babylonian MathsMuch of the basic mathematics we learn today can be traced back thousands of years. In Babylonian times (2000 to 1500 B.C.) quadratic equations could be solved, both by substituting into a general formula and by completing the square. Some cubic equations and biquadratic equations were also discussed. Tablets have been unearthed listing hundreds of unsolved problems involving simultaneous equations. Their algebraic approach to solving geometric problems pre-dates by many centuries the advent of what we now call algebraic geometry. From an 1800 B.C. tablet: An area X, consisting of the sum of two squares, is 1000. The side of one square is 10 less than 2/3 the side of the other square. What are the sides of the squares? Can you solve this problem? Sample problem A large ship manoeuvring towards its berth travels at a speed (in km/hr) of t3 - 3t2 + 4 (starting from t=0). How long does it take to come to a stop? How far does it travel over that period of time? |
MATH151 General MathematicsFirst Semester, Summer School, 18 points Paper detailsThis is an ideal paper for those who need or want to take at least a service paper in mathematical methods and do not yet have a background in mathematics sufficiently strong to join the MATH 160 class. Emphasis is placed on understanding via examples, and you will use the methods taught to study a variety of practical problems. In the process your manipulation skills in algebra and calculus will improve, and you will gain insight into the usefulness of the techniques. It will also provide you with an appreciation of the value and power of Mathematics and the motivation to progress to further MATH papers.In particular you will cover such topics as linear and quadratic models, linear programming, functional notation, differentiation, rates of change, graphing of functions, optimization problems, exponentials and logarithms, compound interest, exponential growth and decay, simple integration. Potential studentsThis course is intended for students whose mathematical background is insufficient to embark on MATH 160 but who need or want to improve their skills, either to assist in their studies of other subjects or to prepare themselves to take MATH 160. Students who have gained 12 credits in NCEA Level 3 Calculus or 18 credits in NCEA Level 3 Statistics and Modelling or an equivalent qualification, will not normally be accepted into this course (for which HOD approval is required).Main topics
PrerequisitesSixth form mathematicsRequired textMath 151 Outline Notes (available at the Print Shop)Useful referencesReviewing of texts for 6th and 7th form mathematics will be useful from time to time. There are also two books available on close reserve at the Science Library, Foundation Maths and Maths for Higher Education.LecturerDr John Curran, room 214LecturesLectures: Tuesday, Wednesday and Thursday at 1 pmTutorialOne two-hour tutorial per week. Either Tues 10-12 or Tues 3-5pmInternal Assessment(Semester 1) There are four computer Skills Tests which count 20% (T) of your final mark. Your internal assessment mark A counts 15% and is based on 10 assignments, the first part of which is completed in the weekly two-hour tutorial and the second part is a weekly take-home exercise. The remaining 65% of the final mark comes from the examination.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 a mark of 5 or better on the first three Skills Tests.Final markThe final mark F is calculated from:F = E + A + T where E (exam mark) is out of 65, A (internal assessment) is out of 15, T (test mark) is out of 20.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.
| |
