MAT2003 Continuous mathematics for computer science - Semester 2, 2015

Probability and combinatorics: elementary probability theory, random variables, probability distributions, expected value; counting arguments in combinatorics; statistics. Linear algebra: vectors and matrices, matrix algebra with applications to flow problems and Markov chains; matrix inversion methods. Calculus: differentiation and partial differentiation; constructing Taylor series expansions.

Mode of Delivery

• Clayton (Day)
• Malaysia (Day)

Workload Requirements

Minimum total expected workload equals 12 hours per week comprising:

(a.) Contact hours for on-campus students:

• Three hours of lectures
• One 1-hour laboratory

(b.) Additional requirements (all students):

• A minimum of 8 hours independent study per week for completing lab and project work, private study and revision.

See also Unit timetable information

Unit Relationships

Prohibitions

ENG1091, MAT1841, MTH1030

Chief Examiner

Campus Lecturer

Your feedback to Us

Previous Student Evaluations of this Unit

Previous feedback has shown satisfaction with this unit, and has not suggested that improvements are needed.

Academic Overview

Learning Outcomes

On successful completion of this unit, students should be able to:

1. apply counting principles in combinatorics and derive key combinatorial identities;
2. describe the principles of elementary probability theory, evaluate conditional probabilities and use Bayes' Theorem;
3. recognise some standard probability density functions, calculate their mean, variance and standard deviation, demonstrate their properties and apply them to relevant problems;
4. implement the principles of experimental design based on those probability density functions, and apply confidence intervals to sample statistics;
5. demonstrate basic knowledge and skills of linear algebra, including to manipulate matrices, solve linear systems, and evaluate and apply determinants;
6. apply knowledge of linear algebra to relevant problems, such as network flow and Markov chains;
7. describe fundamental knowledge of calculus including to differentiate basic, composite, inverse and parametric functions;
8. calculate approximations of functions with tangent lines, evaluate power series and construct Taylor series;
9. perform key skills in the calculus of functions of several variables including to calculate partial derivatives, find tangent planes, identify stationary points and construct Taylor series.

Unit Schedule

Week	Activities	Assessment
0		No formal assessment or activities are undertaken in week 0
1	COMBINATORICS Selections and arrangements, Pascal's Triangle, counting techniques
2	Partitions, combinatorial identities, inclusion and exclusion, pigeonhole principle
3	PROBABILITY Elementary theory, Bayesian analysis, random variables
4	Mean and standard deviation, binomial distribution, normal distribution, t-distribution
5	EXPERIMENTAL DESIGN sampling distributions, confidence intervals	Assignment 1 due
6	LINEAR ALGEBRA Systems of linear equations, Gaussian elimination, Homogeneous systems
7	application to network flow, matrix algebra, Application to Markov Chains
8	Matrix inverses, determinants, application to coding	Assignment 2 due
9	CALCULUS Differentiation, inverse function derivatives, circular functions
10	Parametric differation, higher derivatives, power series and Taylor polynomials
11	Functons of several variables, partial differentiation	Assignment 3 due
12	Tangent planes and linear approximations, higher partial derivatives, Taylor polynomial of degree 2
	SWOT VAC	No formal assessment is undertaken in SWOT VAC
	Examination period	LINK to Assessment Policy: http://policy.monash.edu.au/policy-bank/ academic/education/assessment/ assessment-in-coursework-policy.html

*Unit Schedule details will be maintained and communicated to you via your learning system.

Teaching Approach

Lecture and tutorials or problem classes

Assessment Summary

Examination (3 hours): 70%; In-semester assessment: 30%

Assessment Task	Value	Due Date
Assignment 1	10%	Week 5
Assignment 2	10%	Week 8
Assignment 3	10%	Week 11
Examination 1	70%	To be advised

Assessment Requirements

Assessment Policy

Assessment Tasks

Participation

• Assessment task 1

  Title:

  Assignment 1

  Description:

  Learning Outcomes: 1.   For this assignment, you will answer questions on combinatorics, showing all working and clearly showing all steps.

  Weighting:

  10%

  Criteria for assessment:

  • Assignments are judged on correctness of the answers   and
  • Valid calculations and mathematical arguments to obtain those answers.

  Due date:

  Week 5

• Assessment task 2

  Title:

  Assignment 2

  Description:

  Learning Outcomes: 2, 3, 4. For this assignment, you will answer questions on probability and experimental design, showing all working and clearly showing all steps.

  Weighting:

  10%

  Criteria for assessment:

  • Assignments are judged on correctness of the answers   and
  • Valid calculations and mathematical arguments to obtain those answers.

  Due date:

  Week 8

• Assessment task 3

  Title:

  Assignment 3

  Description:

  Learning Outcomes: 5, 6, 7. For this assignment, you will answer questions on linear algebra, showing all working and clearly showing all steps.

  Weighting:

  10%

  Criteria for assessment:

  • Assignments are judged on correctness of the answers   and 
  • Valid calculations and mathematical arguments to obtain those answers.

  Due date:

  Week 11

Examinations

• Examination 1

  Weighting:

  70%

  Length:

  3 hours

  Type (open/closed book):

  Closed book

  Electronic devices allowed in the exam:

  No calculators or other electronic devices are allowed in the exam. Students will not be disadvantaged by not having a calculator. Where a calculation would be needed, the expression to be evaluated can be written and left without evaluation, and marks will not be reduced for no evaluation.

  Remarks:

  Learning Outcomes: All.

Learning resources

Feedback to you

• Informal feedback on progress in labs/tutes
• Graded assignments with comments
• Solutions to tutes, labs and assignments

Extensions and penalties

Returning assignments

Resubmission of assignments

Assignments may not be resubmitted for this unit.

Referencing requirements

Student are referred to the Library Guides for Citing and Referencing at http://guides.lib.monash.edu/content.php?pid=88267&sid=656564.

Assignment submission

Online submission

Electronic submission of assignments is not available for this unit.

Technological Requirements

Students can bring laptops and tablets to class.

Examination material or equipment

Calculators are not permitted.

Other Information

Policies

Graduate Attributes Policy

Student Charter

Student services

Monash University Library

Disability Liaison Unit

Other

Engineers Australia Stage 1 competencies

This unit is a core unit in the Bachelor of Software Engineering accredited by Engineers Australia. Engineers Australia Accreditation Policy of Professional Engineering Programs requires that programs demonstrate how engineering graduates are prepared for entry to the profession and achieve Stage 1 competencies. The following information describes how this unit contributes to the development of these competencies for the Bachelor of Software Engineering. (Note: not all competencies may be emphasised in this unit).

Stage 1 competency	How the compency is developed in this unit
1. Knowledge and Skills base
1.1. Comprehension, theory based understanding of the underpinning natural and physical sciences and the engineering fundamentals applicable to the engineering discipline.	This unit covers continuous mathematics, which is fundamental to describing the theoretical foundations of the engineering discipline. This element of competency is covered by lecture notes, practical exercises and assignments.
1.2. Conceptual understanding of the mathematics, numerical analysis, statistics, and computer and information sciences, which underpin the engineering discipline.	This element of competency is covered as the unit also includes combinatorics, matrices and statistics, which also underpinning the engineering discipline.
1.3. In-depth understanding of specialist bodies of knowledge within the engineering discipline.	Not covered in this unit
1.4. Discernment of knowledge development and research directions within th engineering discipline.	Not covered in this unit
1.5. Knowledge of engineering design practice and contextual factors impacting the engineering discipline.	Not covered in this unit
1.6. Understanding of the scope, principles, norms, accountabilities and bounds of sustainable engineering practice in the specific discipline.	Not covered in this unit
2. Engineering application ability
2.1. Application of established engineering methods to complex engineering problem solving.	Not covered in this unit.
2.2 Fluent application of engineering techniques, tools and resources.	Not covered in this unit.
2.3. Application of systematic engineering synthesis and design processes.	Not covered in this unit.
2.4. Application of systematic approaches to the conduct and management of engineering projects.	Not covered in this unit.
3. Professional and personal attributes
3.1. Ethical conduct and professional accountability.	Not covered in this unit.
3.2. Effective oral and written communication in professional and lay domains.	Precise languages and mathematical notations are employed in lectures and assignments. Students are expected to be able to explain the mathematics to broad audiences.
3.3. Creative, innovative and proactive demeanour.	Developing mathematical solution to a complex problem is inherently a creative endeavour.
3.4. Professional use and management of information.	Not covered in this unit.
3.5. Orderly management of self, and professional conduct.	Not covered in this unit
3.6. Effective team membership and team leadership.	Not covered in this unit

Relationship between Unit Learning Outcomes and BSE Course Outcomes

No.

CO 1

CO 2

CO 3

CO 4

CO 5

CO 6

CO 7

C0 8

CO 9

CO 10

CO 11

CO 12

CO 13

1

X

X

X

X

2

X

X

X

3

X

X

4

X

X

X

X

5

X

X

X

X

6

X

X

X

X

7

X

X

8

X

X

X

9

X

X

X

X

Relationship between Unit Learning Outcomes and Assessments

No.	Assignments	Tests	Practical Exercises	Exam
1	X			X
2	X			X
3	X			X
4	X			X
5	X			X
6	X			X
7	X			X
8				X
9				X