Course Profile for MATH1050 Mathematical Foundations, Semester 2 2002

(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 is Dr. Jan Chabrowski. in room 67-347 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 3259 or by email at jhc@maths.uq.edu.au . You are welcome to ask any questions about the course during consultation hours, (TBA). Unfortunately, tutors are not paid to answer queries out of class hours, so you should contact lecturers directly. If you have questions about your current or future program of study, contact the chief academic advisor, honours advisor or postgraduate advisor . If you have questions about the library email the mathematics librarian, Larah Seivl-Keevers, at the Dorothy Hill Physical Sciences and Engineering Library or visit the library Frequently Asked Questions page accessible from the library Homepage.

Assumed Background

• If have not passed either High School Maths B or MATH1040, then 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: Monday 8am-9am (67-141), Wednesday 9am-10am (3-329), Friday 9am-10am (67-141)
• Practice: Monday 1pm-2pm (67-240) Wednesday 8am-9am (67-240).
• Tutorials: Wed 1-2pm (43-104), Thurs 12-1pm (67-240), Fri 1-2pm 67-240), Fri 2-3pm (68-320).
• Lectures start in week 1. Tutorials and practice classes start in week 2.
• Public holidays: Wed August 14
• Examination period: Revision period is Nov 4-10, Exam period is 11-23 Nov.
• 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.
  • 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 relegated 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

• 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

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 Exam	1 hour	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 time and venue of the assignment will be given in lectures.
• (See the Resources page for sample exams and advice about missed examinations)
• Mid-semester examination This will be held in the lecture time on Friday 13 September. Further details, including a mock version of the test for practise, will be given out in the first half of semester.
• 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.
• ``swot vac'' At the end of semester and prior to exams there is a week of revision week, starting Monday 10 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.
• Plagiarism: Plagiarism is the act of using other author's ideas and words or solutions without acknowledgement. It is a form of cheating and is considered as misconduct under official university policy and may attract severe penalties. You must not engage in plagiarism in any of your assignments. For more information, consult the libarary UseIt on Plagiarism: http://www.library.uq.edu.au/ssah/useits/plaguseit.html.
• 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.

Personal Situation

• Disabilities: Any student with a disability who may require alternative academic arrangements in the course is encouraged to seek advice at the commencement of the semester from a Disability Adviser at Student Support Services.
• Personal Crises: If you feel that problems in your life are interfering with your university performance, you should consult Student Support Services in the Student Union complex. They offer academic and personal support in a confidential environment for free to students. They can provide a letter to give to lecturers which will help your case for a special exam (there is no longer special consideration for examinations), but do not leave it too late. If you are concerned about privacy with regard to medical certificates, please contact the University Health Service. With your permission, the Director will contact your treating practitioner to clarify the extent of your medical condition or other incapacity, and provide lecturers with a report - the Director is bound by confidentiality obligations. In any case, we prefer this course of action, as we are not qualified to assess medical evidence. The procedure outlined here accords with the University's policy on student privacy and confidentiality.

Graduate Attributes

• 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.

1. 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.

2. 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.

3. 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.

4. 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

• You will find that you have seen some of the content of MATH150 before, in Maths B. Often we shall go quickly over what you should know from that, and then extend and deepen the treatment of the material. Don't fall asleep and then wake up and find yourself out of your depth because you switched off! It is most important to understand fully the basic concepts, so that you have a proper foundation for new work. Don't expect to follow every word in every lecture! Sometimes if the working is simple or straightforward, we shall skip parts and leave you to fill in the details --- in which case do so, later. You will need to go over your lecture notes and spend at least as long again working each week as you spend in contact hours. The course is 12 credit points, which in theory means 12 hours work a week, 5 of which are in the form of class contact. (And 12-5=....) We stress again, please do NOT leave problems, but tell us about anything which isn't going well. The earlier problems are tackled, the easier a resolution will be. It takes time to adjust to lectures in large groups, and university life in general, so it is natural to find it strange at first. Mature age students may also find the experience with large lecture groups is strange and impersonal, so try to be patient in the early weeks. Finally, please note that learning takes place best in an atmosphere of cooperation and mutual help. This applies particularly to courses with large lecture classes, and talking once the lecture is underway should be restricted to the absolute minimum.
• HAVE FUN WITH MATH1050!! Mathematics is a great and exciting broad field, and you should find it rewarding both in the immediate future and later, for wider employment possibilities. Good luck!