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The University of Queensland
Department of Mathematics
Semester 1, 2003

MATH1050 – Mathematical Foundations

Course Profile

Extended Course Profile for MATH1050 Mathematical Foundations,
Semester 1, 2003 (2 unit, 3L 1T)

Course Objective

• This course aims to consolidate students' knowledge and skills in calculus and linear algebra, and to extend this knowledge to provide a firm basis for further study in mathematics.

Contact and Advice

• The course coordinator for Semester 1, 2003 is Mike Pemberton in room 67-451 in the Priestley Building, (building 67). If you have any comments or suggestions on the course or have questions on the course material, contact the coordinator by phone on 3365 3263 or by email at mrp[at]maths.uq.edu.au . You are welcome to ask any questions about the course during consultation hours: TBA. If you have questions about your current or future program of study, contact the chief academic advisor, Dr G. Chandler. If you have questions about the library email the mathematics librarian, Leith Woodall, at the Dorothy Hill Physical Sciences and Engineering Library or visit the library Frequently Asked Questions page, http://www.library.uq.edu.au/skills/question.html, accessible from the library Homepage, http://www.library.uq.edu.au/index.html.

Assumed Background

• If have not passed either High School Maths B or MATH1040, then you must take MATH1040 as a companion course. It is a student's own responsibility to fill in any gaps in their assumed knowledge. You may need to undertake background reading to understand the lecture material.

Teaching Mode

• Three hours of lectures and one hour of tutorial and one hour of practice class (listed as a contact hour) per week.
• All classes start on the hour and conclude at 50 minutes past the hour.
• Lectures start in week 1. Tutorials and Contact classes start in week 2.
• Public holidays: 18/4, 5/5. Mid-semester break: 21/4 to 25/4.
• Examination period: Revision period is 9/6 to 14/6, Exam period is 16/6 to 28/6.
• The purposes of the various forms of class contact are as follows:
  • Lectures define the course material; they set out the basic theory and demonstrate techniques for problem solving. They cover all the basic material required for the course. They are also used to provide information on the organisation of this course.
  • Tutorials give small group assistance on assignment work and any problems you may have. You hand in your assignments to your tutor at the weekly tutorial (and so it is important to know your tutorial group and tutor's name) and receive back marked assignments from your tutor.
  • Contact (practise) classes will be to medium-sized groups, and will cover further examples based on course matter covered in lectures. Depending upon demand, some of the practise class time will be devoted to answering common questions from the group jointly, on the boards.

Calculator Policy

• Some students have Graphics Calculators which they used in high school. While we will not discuss, use, or supply Graphics Calculators, students may use them for their work and in exams. However, the contents of memory must be erased for the exam.

Syllabus

The following list of topics for MATH1050 is intended as a guide only. It is not a strict list of topics in order, and may be varied at times as the semester proceeds.

• Real numbers, complex numbers, functions. Intermediate value theorem, absolute value function, inequalities.
• Polar coordinates
• Linear, exponential and power functions
• GPs, sum to infinity.
• Derivatives, limits, continuity, including definitions
• Techniques of differentiation, related rates
• Greatest and least values of functions.
• Properties of continuous and differentiable functions.
• Revision of the definition of the integral, techniques for indefinite integration.
• Vectors
• Linear equations, matrices.
• Inverse matrices, transpose, determinants.

Additional Help

Tutors are not available for consultation outside the actual tutorial hour. In special cases, if you ask your lecturer first, permission may be given for you to attend an extra tutorial for further help (if your timetable permits this) but please continue to attend one fixed tutorial time each week for the handing-in of assignment work. Please see your lecturer with any problems outside the tutorial times. See your lecturer's door for times when they are available. There are set consultation times for students (see above), although you can make an appointment for a different time if you are unable to come during these set consultation times. Appointments for a mutually convenient time can be made by email or a note under the door with your phone number for contact, or by asking the general office.

Information Changes

• Any changes to course information will be announced in lectures and the information will be reproduced on the web page ( http://www.maths.uq.edu.au/courses/MATH1050). It is your responsibility to keep up to date with all information presented in your lecture group.

Resources

• Course Notes: Notes are available at the course web page. The textbook is also a very important resource (you should acquire a copy).
• Text: The compulsory text is Calculus 4th ed, 1999, by J. Stewart, Phys Sci & Engin. QA303 .S8825 1999
• References: For the linear algebra (matrices) section of MATH1050: Introduction to linear algebra, by Gilbert Strang Wellesley, MA : Wellesley-Cambridge Press, 1998 Edition 2nd ed Phys Sci & Engin KAD QA184 .S78 1998
• Both these books are textbooks for MATH1051 and MATH1052 so you may wish to buy both of them. Second hand copies may well be available. Notes and problems sheets for MATH1050 are available from the WEB and hard copies of problem sheets and solutions will be distributed in lectures. You may buy hard copies of the notes from the photocopy shop in the Student Union.
• Further Reading: If you find the course material difficult to follow and if the set textbook does not help you, you could try looking at other books which cover similar material at this level. See some of the following, in the Physical Sciences and Engineering Library:
  • Calculus: single and multivariable; Deborah Hughes-Hallett ... [et al.]; with the assistance of Adrian Iovita, Otto K. Bretscher, Brad Mann. New York: Wiley, 1998. 2nd ed.
  • Calculus and Analytic Geometry, Thomas and Finney, Addison Wesley.
  • Calculus with Analytic Geometry, Swokowski, Prindle Weber and Schmidt.
  • Elementary Linear Algebra, Anton and Rorres, Wiley and Sons.
  • Many textbooks can be found in the library under QA303 for Calculus, and QA184 for Linear Algebra.
  • Web: The course web page is at http://www.maths.uq.edu.au/courses/MATH1050. Information about the course and other resources are available there.
• High school material: Your school Maths B text may also still be useful, and a Maths C textbook if you have one. The following two books have been used by high schools for Maths C.
  • Q maths 11C, Ross Brodie, Stephen Swift. Publisher Brisbane : Moreton Bay Publishing, 1994- 1994 Edition Phys Sci & Engin QA14.A8 Q6 1994- v.11C
  • Q maths 12C, Ross Brodie, Stephen Swift. Publisher Brisbane : Moreton Bay Publishing, 1994- 1994 Edition Phys Sci & Engin QA14.A8 Q6 1994- v.12C

Assessment

• Assessment will be based on the following two components:

  Assessment Item	Brief Description	Weighting
  		Option 1	Option 2
  Mid-semester Assessment	Two Assessment Items each carrying 15%	30 %	0 %
  End of semester Exam	2 hours	70 %	100 %

• There will also be a library assignment, and in borderline cases, this may be used at the discretion of the lecturer to upgrade your final mark. The library assignment is due at your tutorial in the week 7^th to 11^th April, 2003.
• Mid-semester assessment will consist of 2 Assessment Items which can be downloaded from the following links.
  Assessment Item 1
  Assessment Item 2
• End of semester examination The final exam is closed book 2 hours long plus 10 minutes for perusal, and will be held in the usual examination period. It is timetabled centrally by examinations section, and your lecturers have no power over the choice of the date or time! Calculators without ASCII capabilities are permitted.
• (See the Resources page for sample exams)
• ``swot vac'' At the end of semester and prior to exams there is a week of revision week, starting Monday 9 June.
• Each week you should attempt problems from the current tutorial sheet in your own time before going to the weekly tutorial. You can ask for help with problems at the tutorial, and sometimes your tutor may work through common problems on the board for the benefit of the whole tutorial group.
• The setting-out of your mathematics is important, and you should write your mathematics in sentences! Certainly abbreviations may be used, but your work should still be grammatically correct and coherent. Weekly tutorials are one of the main opportunities that you have to obtain help with your problems. In order to obtain the maximum benefit from these sessions, you should try tutorial sheet problems beforehand. You should bring your lecture notes and tutorial sheets as well as your attempts at solving these problems with you to show your tutor. Remember that your tutor does not attend your lectures, and so although they will be familiar with the whole content of MATH1050, they may not know that last Wednesday you covered substitutions in differentation! Tutors do not usually accept late assignments, so please hand in your work on time! If you find that you are not getting the help you expect from tutorials, please raise your concerns with either me or with a member of staff in the general office. They can send you to an intermediate person to help resolve any difficulties you may encounter.
• Missed assessment items: Failure to complete any item of assessment will result in your receiving no credit for that component of the assessment.
• For information on Plagiarism, Help available for students with disabilities, University policy on Special and Supplementary Examinations, Feedback on Assessment, Assistance for students, or The student Liason Officer, visit http://spider.sps.uq.edu.au/course_profile_info.pdf
• Assessment Criteria:
  • Solutions will be marked for accuracy, appropriateness of mathematical techniques and clarity of presentation, as demonstrated by examples presented in lectures. To earn a Grade of 7, a student must demonstrate an excellent understanding of MATH1050. This includes clear expression of nearly all their deductions and explanations, the use of appropriate and efficient mathematical techniques and accurate answers to nearly all questions and tasks with appropriate justification. They will be able to apply techniques to completely solve both theoretical and practical problems.
  • To earn a Grade of 6, a student must demonstrate a comprehensive understanding of MATH1050. This includes clear expression of most of their deductions and explanations, the general use of appropriate and efficient mathematical techniques and accurate answers to most questions and tasks with appropriate justification. They will be able to apply techniques to partially solve both theoretical and practical problems.
  • To earn a Grade of 5, a student must demonstrate an adequate understanding of MATH1050. This includes clear expression of some of their deductions and explanations, the use of appropriate and efficient mathematical techniques in some situations and accurate answers to some questions and tasks with appropriate justification. They will be able to apply techniques to solve fundamental problems.
  • To earn a Grade of 4, a student must demonstrat an understanding of the basic concepts of MATH1050. This includes occasionally expressing their deductions and explanations clearly, the occasional use of appropriate and efficient mathematical techniques and accurate answers to a few questions and tasks with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems and applied this knowledge in some cases.
  • To earn a Grade of 3, a student must demonstrate some knowledge of the basic concepts of MATH1050. This includes occasional expression of their deductions and explanations, the use of a few appropriate and efficient mathematical techniques and attempts to answer a few questions and tasks accurately and with appropriate justification. They will have demonstrated knowledge of techniques used to solve problems.
  • To earn a Grade of 2, a student must demonstrate some knowledge of the basic concepts of MATH1050. This includes attempts at expressing their deductions and explanations and attempts to answer a few questions accurately.
  • A student will receive a Grade of 1 if they demonstrate extremely poor knowledge of the basic concepts in the course material. This includes attempts at answering some questions but showing an extremely poor understanding of the key concepts.

Graduate Attributes

1. • You will get an in-depth understanding of the foundation mathematical techniques as described in the course content.
   • You will achieve an understanding of the breadth of mathematics.
   • You will obtain an understanding of the applications of mathematics to other fields.

2. Effective Communication

   • You will gain the ability to present a logical sequence of reasoning using appropriate mathematical notation and language.
   • You will get the ability to select and use an appropriate level, style and means of written communication, using the symbolic, graphical, and diagrammatic forms relevant to the context.
   • You will obtain the ability to effectively and appropriately use the library and some information technologies.

3. Independence and Creativity

   • You will improve your ability to work and learn independently.
   • You will get the ability to generate and synthesise ideas and adapt innovatively to changing environments.
   • You will obtain the ability to formulate problems mathematically.

4. Critical Judgement

   • You will improve your ability to identify and define problems.
   • You will get the ability to evaluate methodologies and models, to make decisions and to reflect critically on the mathematical bases for these decisions.
   • You will improve your ability to apply critical reasoning to analyse and evaluate a piece of mathematics.

5. Ethical and Social Understanding

   • Students will obtain knowledge and respect of ethical standards in relation to working in the area of mathematics.
   • You will get an appreciation of the history of mathematics as an ongoing human endeavour.

Some Final Advice

• Often we revise Maths B work in MATH1050. This revision in usually quick and important so stay focussed. Don't expect to follow every word in every lecture! Sometimes we skip simple or stragihtforward parts and leave you to fill in the details --- in which case do so, later. We expect that a two unit course takes a total of about 12 hours work a week. Seek early help with problems; do NOT leave problems until later.
• Enjoy MATH1050!! Good luck with all your studies this year!

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