Mathematics units

University of Tasmania
Mathematics Units - 1996


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Mathematics - Department of Mathematics at Hobart

The Department of Mathematics offers units for students specialising in mathematics and for those who need or want to include mathematics in their study of other disciplines. Most first year units require TCE Mathematics Stage 2 as a prerequisite, though some will accept either TCE Mathematics Stage 2 or TCE Mathematics Applied.
Selecting the Mathematics units
The units that students choose will depend on their major study. Mathematics is divided into the following 'parcels' of units:
Mathematics 1, Mathematics 2, Mathematics 3
Discrete Mathematics 1, Discrete Mathematics 2, Discrete Mathematics 3
Basic Mathematics,
Mathematics 2C, Mathematics 3C.
Students may choose to study one or two of these parcels, or they may choose individual units. Not all units are necessarily offered each year. The following are recommended:
For a double major in Mathematics:

Year 1: Mathematics 1 and Discrete Mathematics 1
Year 2: Mathematics 2 and Discrete Mathematics 2
Year 3: Mathematics 3 and Discrete Mathematics 3

For majors in Mathematics and a Physical Science:

Year 1: Mathematics 1
Year 2: Mathematics 2
Year 3: Mathematics 3

For majors in Mathematics and Computer Science:

Year 1: Discrete Mathematics 1
Year 2: Discrete Mathematics 2
Year 3: Discrete Mathematics 3

For majors in non-physical Sciences:

Year 1: Basic Mathematics
Year 2: Selected units of Discrete Mathematics 2
Year 3: Selected units of Discrete Mathematics 3

For majors in Economics:

Year 1: Mathematics 1 or Basic Mathematics 1
Year 2: Mathematics 2 or Discrete Mathematics 2
Year 3: Selected units of Mathematics 3C

For High School or College Mathematics Teaching:

Year 1: Mathematics 1
Year 2: Mathematics 2 and at least 16.67% Discrete Mathematics 2
Year 3: Mathematics 3C

For those with an interest in statistics

KMA151 Applied Statistics 1,
KMA205 Principles of Statistics 2,
KMA251 Applied Statistics 2,
KMA312 Applied Statistics 3 are recommended.

The units which go to make up the various parcels are as follows:

Year 1
Mathematics 1
Either KMA102 or KMA105
KMA102 Calculus and Linear Algebra 1 [25%]
KMA105 Calculus and Linear Algebra 1S [25%]

Discrete Mathematics 1
25% chosen from:
KMA103 Linear Algebra [8.33%]
KMA107 Mathematics for Computer Science [8.33%]
KMA115 Discrete Modelling 1 [8.33%]
KMA151 Applied Statistics 1 [8.33%]

Basic Mathematics
(Cannot be taken with Mathematics 1)
KMA122 General Mathematics [16.67%]
plus one of:
KMA107 Mathematics for Computer Science [8.33%]
KMA115 Discrete Modelling 1 8.33%]
KMA151 Applied Statistics 1 [8.33%]

Year 2
Mathematics 2
KMA202 Calculus and Linear Algebra 2 [16.67%]
plus 16.67% chosen from:
KMA203 Algebra [8.33%]
KMA204 Analysis [8.33%]
KMA205 Principles of Statistics 2 [8.33%]
KMA213 Differential Equations [8.33%]

Discrete Mathematics 2
33.33% chosen from:
KMA203 Algebra [8.33%]
KMA205 Principles of Statistics 2 [8.33%]
KMA224 Discrete Modelling 2A [8.33%]
KMA225 Discrete Modelling 2B [8.33%]
KMA251 Applied Statistics 2 [8.33%]
N.B. KMA203 requires KMA103 or KMA102 or KMA105 as a prerequisite.
KMA205 requires TCE Mathematics Stage 2 (i.e. some Calculus) as a prerequisite.


Mathematics 2C
33.33% chosen from year-two units:
KMA202 Calculus and Linear Algebra 2 [16.67%]
KMA203 Algebra [8.33%]
KMA204 Analysis [8.33%]
KMA205 Principles of Statistics 2 [8.33%]
KMA213 Differential Equations [8.33%]
KMA224 Discrete Modelling 2A [8.33%]
KMA225 Discrete Modelling 2B [8.33%]
KMA251 Applied Statistics 2 [8.33%]
KMA260 Mathematics for Engineers 2 [19%]
KMA270 Mathematics for Engineers 2A [9.5%]

Year 3
Mathematics 3
KMA301 Analysis 3 [16.67%]
KMA314 Partial Differential Equations [8.33%]
KMA331 Analysis of Numerical Methods [8.33%]
KMA332 Complex Variables [8.33%]
KMA341 Computational Techniques [8.33%]

Discrete Mathematics 3
50% chosen from:
KMA303 Algebra 3 [16.67%]
KMA304 Geometry [16.67%]
KMA312 Applied Statistics 3 [16.67%]
KMA315 Discrete Modelling 3 [16.67%]

Mathematics 3C
50% chosen from year-three units:
KMA301 Analysis 3 [16.67%]
KMA303 Algebra 3 [16.67%]
KMA304 Geometry [16.67%]
KMA310 Mathematics for Surveyors 3 [15.6%]
KMA312 Applied Statistics 3 [16.67%]
KMA314 Partial Differential Equations [8.33%]
KMA315 Discrete Modelling 3 [16.67%]
KMA331 Analysis of Numerical Methods [8.33%]
KMA332 Complex Variables [8.33%]
KMA341 Computational Techniques [8.33%]

For Humanities and Social Science students the following units are available:

Year 1
KMA110 Mathematics 1 [25%] (consisting of KMA102 or KMA105)
KMA114 Discrete Mathematics 1 [25%] (consisting of any three of KMA103, KMA107, KMA115, KMA151)
KMA117 Basic Mathematics [25%] (consisting of KMA122 plus one of KMA107, KMA115, KMA151)

Year 2
KMA200 Mathematics 2 [33.33%] (consisting of KMA202 plus any two of KMA203, KMA204, KMA205, KMA213)
KMA223 Discrete Mathematics 2 [33.33%] (consisting of any four of KMA203, KMA205, KMA224, KMA225, KMA251)
KMA229 Mathematics 2C [33.33%] (consisting of any combination of year-two units forming a 33.33% loading approved by the Mathematics HoD)

Year 3
KMA370 Mathematics 3 [50%] (consisting of KMA301, KMA331, KMA332, KMA314, KMA341)
KMA316 Discrete Mathematics 3 [50%] (consisting of any three of KMA303, KMA304, KMA312, KMA315)
KMA375 Mathematics 3C [50%] (consisting of any combination of third-year units forming a 50% loading, approved by the Mathematics HoD).

Students should take careful note of the prerequisites and corequisites of each unit (see unit descriptions and details below). If they are in any doubt as to the suitability of a unit, students should consult a staff member of the Department of Mathematics. Prerequisites can be waived by the Head of Department alone. Some unit combinations involve timetable clashes. Students are urged to check the timetable before discussing their proposed course with the departmental representative. They will be required to show a completed timetable when seeking final approval of their enrolment.
The usual minimum requirement for admission to Mathematics Honours is 50% year-three Mathematics units including either KMA303 or KMA301. However, special arrangements can be made for students without either of these units.
Students should note that not all units are offered in any one year. Before selecting third-year units, students are advised to discuss their proposed courses with members of the lecturing staff of the department.
Unit descriptions

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© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA102 Calculus and Linear Algebra 1

Prepares students for subsequent studies in analysis-based mathematics and other disciplines, which require a solid grounding in mathematical skills of both a theoretical and practical nature. Studies include: (a) Calculus - real numbers, functions, sequences and series; trigonometric and exponential functions and their inverses; conic sections, graphs, curves and level sets; properties and applications of differentiation and integration; Mean Value Theorems, Taylor's Theorem and Taylor series; differentiation of vector-valued functions; introduction to functions of several variables; first and second order linear differential equations; (b) Symbolic computation - introduction to the use of Mathematica as an environment for doing mathematics; and (c) Linear Algebra - systems of linear equations, matrices and determinants; introduction to vectors and vector spaces, dot products, linear transformations, and complex numbers.

Special Notes
teaching staff Miss HL Chick, Mr D Fearnley-Sander and Dr JD Donaldson
campus & mode Hbt, int
unit weight [25% (9pts)]
teaching pattern full year - 4x1-hour lectures and a 1-hour tutorial a week (28 weeks)
prerequisites TCE Mathematics Stage 2 (or HSC Mathematics III)
corequisites
mutual exclusions KMA105, KMA103, KMA122
method of assessment assignments and other coursework (20%); three 2-hour exams: one mid-year and two in Nov (80%)
required texts, etc
Adams RA, Calculus, a Complete Course, Addison-Wesley, 1991.
recommended reading
Course: Bachelor of Computing (S3H)
Bachelor of Science specimen course - Physical Sciences, Psychology or Humanities (S3G)
Bachelor of Science specimen course - Geological Sciences (S3G)
Bachelor of Science (S3G)



Staff of the Department of Mathematics
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© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA103 Linear Algebra

Focuses on systems of linear equations, matrices and determinants, and an introduction to vectors and vector spaces, dot products, linear transformations, and complex numbers.

Special Notes
teaching staff Miss HL Chick
campus & mode Hbt, int
unit weight [8.33% (3pts]
teaching pattern full year - 1-hour lecture and 1-hour tutorial a week (28 weeks)
prerequisites TCE Mathematics Stage 2 (or HSC Mathematics III)
corequisites
mutual exclusions KMA102, KMA105, KMA122
method of assessment assignments and other internal assessment (20%); one 2-hour exam in Nov (80%)
required texts, etc
a set of printed notes that supplement the lectures will be available for purchase. Details will be announced in the first lecture.
recommended reading
Course: Bachelor of Computing (S3H)
Bachelor of Science specimen course - Computer Science and Mathematics (S3G)
Bachelor of Science (S3G) - main schedule of units




Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA105 Calculus and Linear Algebra 1S

Is for students who have achieved a high level qualification in pre-tertiary mathematics, preparing them for subsequent studies in analysis-based mathematics and other disciplines, which require a solid grounding in mathematical skills of both a theoretical and practical nature. Studies include: (a) Calculus - methods of proof, functions and formal definitions of limits and continuity, differential and integral calculus of functions of a single variable, elementary differential equations, sequences and series including Taylor's theorem; (b) Symbolic computation - introduction to the use of Mathematica as an environment for doing mathematics; and (c) Linear Algebra - systems of linear equations, matrices and determinants; introduction to vectors and vector spaces, dot products, linear transformations, and complex numbers.

Special Notes offered subject to sufficient numbers enrolling

teaching staff
campus & mode Hbt, int
unit weight [25% (9pts)]
teaching pattern full year - 4x1-hour lectures, a 1- hour tutorial a week (28 weeks)
prerequisites TCE Maths Stage 3 or Stage 2 with permission of HoD
corequisites
mutual exclusions KMA102, KMA103
method of assessment
required texts, etc
Apostol TM, Calculus, Vol 1, 2nd edn, John Wiley & Sons, New York, 1967.
recommended reading
Course: Bachelor of Computing (S3H)
Bachelor of Science (S3G) - main schedule of units





Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA107 Mathematics for Computer Science

Introduces some topics that are fundamental to mathematics and computer science: basic logic, functions, relations and algebraic systems, including Boolean algebras.

Special Notes
teaching staff Mr D Fearnley-Sander
campus & mode Hbt, int
unit weight [8.33% (3pts)]
teaching pattern sem 2 - 2x1-hour lectures and a 1-hour tutorial a week (14 weeks)
prerequisites TCE Mathematics Stage 2 (HSC Mathematics III) or TCE Mathematics Applied (HSC Mathematics Applied III)
corequisites
mutual exclusions
method of assessment 2-hour exam in Nov.
required texts, etc
recommended reading
Course: Bachelor of Computing (S3H)
Bachelor of Science specimen course - Computer Science and Mathematics (S3G)
Bachelor of Science (S3G) - main schedule of units




Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA110 Mathematics 1

Is only for Humanities and Social Sciences students, who study either KMA102 or KMA105 (see above).

Special Notes
teaching staff
campus & mode
unit weight [25%]
teaching pattern full year.
prerequisites
corequisites
mutual exclusions
method of assessment
required texts, etc
recommended reading
Course:






Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA114 Discrete Mathematics 1

Is only for Humanities and Social Sciences students, who study any three of KMA103, KMA107, KMA115, and KMA151.

Special Notes
teaching staff
campus & mode
unit weight [25%]
teaching pattern full year.
prerequisites
corequisites
mutual exclusions
method of assessment
required texts, etc
recommended reading
Course:






Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA115 Discrete Modelling 1

Introduces students to mathematics modelling that is widely applicable to decision making in areas such as business, politics, medicine and manufacturing. For many students, this is the first time they have met with such techniques, and experience shows that irrespective of their background, dedicated students are likely to succeed. The unit focuses mainly on linear programming and elementary probability techniques and applications - geometric solutions, Simplex Method, Duality, Transportation problems, and selected topics from Game Theory, Markov Chains and Difference Equations. The unit prepares students who may want to study Discrete Modelling 2A in their second year.

Special Notes
teaching staff Mrs R Gregory
campus & mode Hbt, int
unit weight [8.33% (3pts)]
teaching pattern sem 1 - 2x1-hour lectures and a 1-hour tutorial a week (14 weeks)
prerequisites TCE Maths Applied or Maths Stage 3 or Stage 2
corequisites
mutual exclusions
method of assessment maximum of [(assignments (20%); 2-hour exam (80%)), (2-hour exam (100%))] ; exam midyearreq: printed lecture notes are distributed in each lecture.
required texts, etc
recommended reading
Course: Bachelor of Computing (S3H)
Bachelor of Science (S3G) - main schedule of units





Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA117 Basic Mathematics

Is only for Humanities and Social Sciences students, who study KMA122 and one of KMA107, KMA115 and KMA151.

Special Notes
teaching staff
campus & mode
unit weight [25%]
teaching pattern full year.
prerequisites
corequisites
mutual exclusions
method of assessment
required texts, etc
recommended reading
Course:






Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA122 General Mathematics

Is for students who need some mathematics to supplement their main course of study (for example, in Life Sciences) but who do not wish to make Mathematics one of their main pursuits. Topics include: functions, properties and applications of differentiation and integration, simple differential equations, and solving systems of linear equations. Emphasis is placed on applications rather than theory.

Special Notes may not be counted as a prerequisite for most second year mathematics units

teaching staff (Coordinator) Miss HL Chick
campus & mode Hbt, int
unit weight [16.67% (6pts)]
teaching pattern full year -2x1-hour lectures and a 1-hour tutorial a week
prerequisites TCE Mathematics Stage 2 or TCE Mathematics Applied
corequisites
mutual exclusions KMA102, KMA103, KMA105
method of assessment 3-hour exam in Nov (80%), assignments (10%); project (10%).
required texts, etc
recommended reading
Course: Bachelor of Computing (S3H)
Bachelor of Science specimen course - Forest Ecology (S3G)
Bachelor of Science (S3G) - main schedule of units




Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.



KMA151 Applied Statistics 1

Is an introduction covering standard statistical methods. Topics are: data analysis, elementary probability, standard distributions, simple statistical tests, linear regression, goodness-of-fit tests, analysis of variance.

Special Notes
teaching staff Dr BM Brown
campus & mode Hbt, int
unit weight [8.33% (3pts)]
teaching pattern sem 2 - 2x1-hour lectures and a 1-hour tutorial a week
prerequisites TCE Mathematics Stage 2 or TCE Mathematics Applied
corequisites
mutual exclusions
method of assessment assignments (up to 20%); 2-hour exam (at least 80%)
required texts, etc
printed lecture notes are available.
recommended reading
Course: Bachelor of Agricultural Science (S3A)
Bachelor of Computing (S3H)
Bachelor of Science specimen course - Computer Science and Mathematics (S3G)
Bachelor of Science specimen course - Forest Ecology (S3G)
Bachelor of Science specimen course - Forest Ecology (S3G)
Bachelor of Science (S3G) - main schedule of units

Staff of the Department of Mathematics
To return to Units Contents Page
To return to Handbooks Home Page

© University of Tasmania, 1996.
Details shown above were correct at the time of publication. While every effort is made to keep this information up to date, the University reserves the right to discontinue or vary courses at any time without notice.

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