Study Guide -- Math 123 -- 1st semester 2008


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Tutorial problem sets 

Assignments

Assignment solutions

Electronic quizzes  If you have problems meeting the deadlines of the electronic quizzes, please contact Garry Lawson.
His email address is  garry@ics.mq.edu.au


Lecture notes by Chen and Duong

Lecture notes by Cooper
Examinable material from the notes by Cooper: Chapters 1 through 12 except 5.6, 5.7, Chapter 8, 10.7, 11.7, and 12.4

past examination papers
 (Note - more past papers may be available at the library, online or as hard copy)

Check your marks

Some material from the Algebra lectures.
 

Lecturers

Chris Meaney, E7A 305, 9850 8922, chrism@maths.mq.edu.au
Gerry Myerson, E7A 406, 9850 8952, gerry@maths.mq.edu.au


Liaison Officer

Garry Lawson, E7A 416, 9850 4175, garry@ics.mq.edu.au


Lecture Times

Lecture 1    Calculus (Myerson)    Tue 10 E7B MASON
Lecture 2    Calculus (Myerson)    Wed 10 X5B T1
Lecture 3    Algebra (Meaney)    Thu 12 E7B MASON
Lecture 4    Algebra (Meaney)    Fri 10 X5B T1

Please note that lectures will often contain material which is not in the unit notes,
so attendance at all lectures is strongly recommended.


Tutorials

Tutorials begin in Week 1.

Problems accessible here.

Tutorials will include examples which may directly assist your preparation for assignments,
tests and the final exam. In tutorials you have the opportunity to ask questions and clarify
anything you don't understand. Your written work will be returned to you during tutorials.

In tutorials you will see more examples than in lectures. The tutors will demonstrate how
to write your solutions in the best way, and encourage you to ask the sorts of questions that
you might not normally ask during lectures.

You should download the tutorial exercises and work on them each week, before attending
your tutorial class. It is important to practice doing mathematical problems yourself, you can't
learn mathematics by just watching somebody else do it.

The tutors may not always be able to get through all the questions during the tutorial, but will
do at least one example of each type. The exercises are intended to give you practice, and by
doing multiple examples you will remember the techniques. We will not provide printed
solutions, it is up to you to attend the tutorials, ask the tutor to do specific questions if you
want them.

To develop independence and initiative as a mathematics student, we encourage you to look
for ways of checking and justifying your solutions, rather than relying on a list of answers such
as you find in a school text-book. Discussing the solutions with other students is an effective
way to learn and to develop your mathematical intuition.


Texts

The main text is the set of lecture notes:

Elementary Mathematics (MATH130 and MATH123) by Chen and Duong

Calculus for MATH123 by C. Cooper

You should download and study these.

The online notes are intended primarily as a source of reference. These are not intended to be treated as the only source for learning.

The same material is covered in many texts. You should try several of these, adopting one which suits your personal style of learning.

The following texts are suggested for reference only, and it is not essential to own copies.

Aufman, Barker and Nation: Precalculus (LIBRARY QA331.3.A8/1993) published by Houghton-Miflin Company, 1993.
Taylor and Gilligan: Applied Calculus (LIBRARY QA303.T204/1996)
James Stewart, Lothar Redlin, Saleem Watson:  Precalculus : mathematics for calculus  (LIBRARY QA39.2 .S75/1998)


The library contains dozens of other books which may be useful, including:

Hughes-Hallet, Gleason et al. Calculus published by Jacaranda-Wiley
Coppins and Umberger, College Mathematics published by Addison-Wesley Inc.
Flanders and Price, Algebra and Trigonometry

Each of these books has been used as a text for courses at this level in previous years.


Topics

Details are subject to change. Check back here from time to time.
Note in particular that there is only one Algebra lecture in week 4 and that will necessitate some jiggling of the schedule.

Algebra

Weeks 1 and 2:  Basic algebra
Week 3: Inequalities and absolute values
Weeks 4 and 5:  Indices, logarithms, and exponential functions
Week 6: Quadratic equations and inequalities
Week 7: Introduction to complex numbers
-------------- mid-semester break ------------------------------
Weeks 8 and 9:  Arithmetic and geometric progressions with applications
Weeks 10 and 11:  Counting techniques (permutations and combinations) and probability
Week 12: Introduction to matrices, application to linear equations
Week 13: Revision (time permitting)

 Calculus

Weeks 1 and 2:  Functions and graphs. Lines, slopes, and intercepts
Week 3: Introduction to differentiation
Week 4: Tangents and normals
Weeks 5 and 6: Maxima and minima. Second derivatives
Weeks 6 and 7: Derivatives of exponential and logarithmic functions
-------------- mid-semester break ------------------------------
Week 8: Newton's method
Week 9: Antidifferentiation, substitution
Week 10: Definite integrals, areas
Week 11: Simple differential equations
Week 12: Numerical integration, Simpson's Rule


Assessment

Five assignments contributing, in total, 10% to your mark
Two tests (20%)
Six quizzes (0% but compulsory)
Final examination (70%)

The level of understanding is reflected in the grade awarded. For an explanation of the grades,
please see Rule 10 of Bachelor Degree Rules, concerning grades, on pages 98-99 in the 2008
Handbook of Undergraduate Studies. Your raw score is used in deciding your grade and will
then be scaled to determine your official mark.


Assignments

There will be five (5) assignments. Each will contain questions relevant to the material
being covered at the time. It is crucial that you make a reasonable attempt on every occasion,
as the assignment questions will be designed to enhance the understanding of the unit. You
must start working on these questions well before the due date, as you may need several
attempts before you solve some of these problems. Do not be discouraged if you cannot solve
them at your first attempt. A good strategy is to spend short amounts of time on several
occasions thinking about them and coming back to them.

You are encouraged to ask your tutor and lecturers for help. Note, however, that they will tend to
answer your questions by asking you questions. In this way, your thinking will be guided,
so that if you come away with a solution it will be you who has worked it out, not them.
You should show your written attempts when asking for help.

It is permissible, and indeed you are encouraged, to discuss assignment questions with your
friends. That does not constitute copying and a lot can be learned this way. However, you
must write out your solutions independently and understand what you are writing. Mindless
copying is easy to detect and may result in disciplinary action.

Assignments are due at 10am Tuesday in weeks 4, 6, 8, 10, and 12. Personalised questions
and cover-pages are to be found on the MATH123 Assignments website. All assignments
must be submitted with the personalised cover page.

Also, throughout the semester you may check your marks.

You must submit your assignments via the relevant assignment boxes. These boxes are
located in the corridor between E7A and E7B, near Room E7B 363. You should use the
coversheet provided for this purpose, available from the MATH 123 assignments website.
Pages should be securely stapled together, or secured within a folder or plastic sleeve. Poorly
presented, or unreadable, work will be given the mark of zero (0). Late assignments will not
be marked; where there is documented medical or other evidence that it has not been possible
to submit in time, a mark consistent with your work on other assignments will be used.

It may be that only selected questions in assignments will be marked. The markers will read
your solutions of these selected questions up to the first serious mistake and then attempt to
make relevant comments. They will not check calculations in detail and will overlook simple
numerical errors if your approach is correct. Model solutions will be posted to the web after
the assignment boxes have been cleared. Assignments will usually be returned in the tutorials
 the following week. Please note that any marked assignment not collected when returned will
be left in the alphabetical pigeonholes near the assignment boxes. These pigeonholes are not
secure, and assignments are known to be lost frequently. The responsibility of the Department
for any such uncollected assignments ceases when they are deposited in the pigeonholes.

Past experience clearly indicates that students who do not attempt assignments throughout the
semester rarely do well in the final examination.


Tests

There will be two tests, designed to check your understanding and monitor your progress.
They will be conducted in the tutorials in weeks 5 and 11.
Worked solutions may be posted on the Web. Students may check their own marks.


Quizzes

Electronic quizzes are provided for revision of basic skills, and practice of new skills
acquired during the course. These are available via the web and must be completed
successfully. They can be found here.

The quizzes may be attempted as many times as you wish within the allocated time;
a different quiz will be generated each time. A quiz is considered completed if there
are at most two questions answered incorrectly. This allows for inadvertent errors that
may be made in questions that require a specific typed answer. Nevertheless, students
should aim to be able to answer all questions correctly -- as there will be no such
leniency in tests, or on the final exam.

Note that the first two of these quizzes are due to be completed within the first 4 weeks of semester.

Students should use these quizzes to help identify any areas of mathematics in which basic skills may be lacking.

The Numeracy Centre is available to help students who wish to consolidate their basic knowledge of mathematics.

Quizzes are due for completion by the Wednesday night (midnight) of the following weeks:

Quiz 1 week 3 revision of basic skills #1
Quiz 2 week 4 revision of basic skills #2
Quiz 3 week 7 equations, lines, derivatives
Quiz 4 week 9 inequalities, absolute values, logarithms, complex numbers
Quiz 5 week 11 arithmetic and geometric progressions, integration
Quiz 6 week 13 counting techniques, matrices.

If you cannot complete a quiz in time, please consult Garry Lawson (the Mathematics Undergraduate Liaison Officer,
contact details given above) for advice.

Students must pass all quizzes by the due date or have made alternative arrangements with Garry Lawson.
No grade better than `PC'(49) will be awarded to any student who has not successfully
completed all the quizzes.

In case of problems accessing the quizzes from your home computer, do the quizzes on campus,
in the Library, at the Numeracy Centre or in the C5C or E6A computing labs. Having technical
problems with your home computer does not constitute a reasonable excuse for not having
completed a quiz by the deadline. You are advised to start work early!

These quizzes have been specially developed for use with Mathematics courses at Macquarie
University. They require reasonably recent computers and software versions of some common
(freely available) software programs. It is possible that technical difficulties may occur when
using old versions of Adobe Reader software. Should difficulties be encountered when using
home computers, then students are advised to try again from on-campus installations, such as
in the library or the various computing laboratories.

Further electronic quizzes, covering recently taught material, will become available later
throughout the semester. Successful completion of these quizzes constitutes part of the compulsory
requirements of this course.


Exam

There will be a three-hour, comprehensive final exam.

Calculators, but not the `graphing' kind, will be allowed to be used in the exam. Students should
consider buying a non-graphing calculator as well, if they normally use a graphing one. Mobile
phones are not allowed in exams.

Some past examination papers are available for study.


Serious problems

If a medical or other serious problem prevents you from completing a task on time, or causes
you to miss several classes, you should submit an `Advice of Absence' form to the Student
Enquiry Service as soon as possible, accompanied by supporting documentation such as
a medical certificate.


Withdrawal

Your attention is drawn to the following deadline:

Monday 31 March: Last day for students to lodge a "Change of Program" form to discontinue the unit.
See pages 99-100 of the 2008 Macquarie University Handbook of Undergraduate Studies. See also
page 41 concerning "unavoidable disruption".


Plagiarism

Plagiarism involves using the work of another person and presenting it as one's own.
Any of the following acts constitutes plagiarism unless the source of each quotation
or piece of borrowed material is clearly acknowledged:
Encouraging or assisting another person to commit plagiarism is a form of improper collusion and may attract the same penalties that apply to plagiarism.

Any student suspected of plagiarism may be asked for an explanation in the first instance. If no satisfactory explanation is forthcoming, the student may be penalized
by being awarded negative full marks for the assignment(s) concerned. Any further infringement will be reported to the University for consideration by the Disciplinary Committee.

Please see the section concerning plagiarism on pages 47–48 in the 2008 Handbook of Undergraduate Studies.


Special Consideration

If illness or misadventure make it impossible for you to sit for the final examination, or interfere
significantly with your performance in the examination, you are permitted to request
"special consideration". If we are satisfied (e.g., by your previous performance in the unit, or by
the quality of work you have been able to produce in the examination) that there is evidence
that you have not been able to show your true ability, we may decide to invite you to sit for
a special examination to resolve your grade for the unit.

Special consideration will only be given to students who have
Please contact one of the lecturers in case of difficulty over any of these.

It is the Division's decision whether to offer a special examination or not. Students cannot apply
for one, or expect to be granted one automatically, and requests "to sit for the special exam"
will not be looked upon with favour.

It is essential that you notify the Registrar in writing of the misadventure, accompanied by any
appropriate documentary evidence. It is also advisable for you to let us know informally that you
have applied to the Registrar.

The purpose of the special examination is to resolve the temporary difficulty caused by your illness
or misadventure; the purpose is not to give you an advantage over other students by allowing you
extra time to study. For this reason we will hold the special examination as soon as possible, and
in determining your grade for a special examination we may take into account the possibility of
extra study time available to you.

In view of the previous paragraph, you must make sure you are readily contactable, and must hold
yourself available to sit for the exam at short notice on the date and time we set. Address information
provided to the Registrar must be up to date.

It is expected that if there is a Special Examination then it will be held on Friday 11 July 9.20 am at a location which will be specified closer to that date.

If you elect to be away from Sydney during the week of the special examination, and so cannot
be contacted or are unavailable to sit for the examination, we will accept this as a firm indication
that any request you may have submitted for special consideration does not apply to this unit.


Learning Outcomes and Grades

The outcome of this unit is an understanding of the various topics that are presented.

The level of understanding is reflected in the grade awarded.

For an explanation of the grades, please see Rule 10 of Bachelor Degree Rules, concerning grades,
on pages 98–99 in the 2008 Handbook of Undergraduate Studies.


Generic Skills

The Macquarie experience is designed to lead students to a career in the city and a place in the world.
It encourages life-long learning and links teaching to cutting-edge research.

Macquarie seeks to develop generic skills for students, building flexible outcomes for life
and for the workplace over a life's career. These skills include:

foundation skills of literacy, numeracy and information technology;
self-awareness and interpersonal skills, such as the capacity for self-management, collaboration
and leadership;
communication skills for effective presentation and cultural understanding;
critical analysis skills to evaluate, synthesise and judge;
problem-solving skills to apply and adapt knowledge to the real world; and
creative thinking skills to imagine, invent and discover.

Mathematics is an ideal medium to learn problem solving skills. Many problems occurring in
the real world can be described as mathematical problems, and are then investigated thoroughly
using all the mathematical techniques available. The solutions are then interpreted in suitable ways
to provide answers to the original problems. In this unit, you will be trained in a number of these
mathematical techniques, as well as some of the ways to apply them.