Faculty of Science

School of Mathematics and Statistics

MATH1014: Introduction to Linear Algebra

Semester 2, 2014 | 3 Credit Points | Coordinator: Dr David Easdown(david.easdown@sydney.edu.au)

1 Introduction

MATH1014 is a 3 credit point unit of study that provides an Introduction to Linear Algebraand its applications. Linear algebra and calculus are the two central themes of undergraduatemathematics. Linear algebra is the study of vectors, vector spaces, linear maps, and systems oflinear equations. It has extensive applications in the natural sciences and the social sciences,since nonlinear models can often be approximated by linear ones. In this unit, students will beintroduced to the basic tools and techniques that are used in linear algebra. Topics coveredinclude:

Geometry and Algebra of Vectors: Length and angle, lines and planes; Modular arithmeticand codes;Linear equations: Systems of linear equations, Gaussian and Gauss-Jordan elimination;Resource allocation and network analysis;Matrices and Linear Algebra: Matrix operations, matrix algebra, invertible matrices; Lesliepopulation models and Markov chains;Eigenvalues, Eigenvalues and Determinants: Introduction to eigenvalues and eigenvectors,determinants; Application to population models and Markov chains.

1.1 Assumed Knowledge and Prohibitions

Assumed knowledge: HSC Mathematics or MATH1111.

Students who wish to enrol in this unit without the assumed knowledge will need to do aBridging Course in February. Details of Bridging Courses are available from the StudentServices Office, or from mathematics advisers at enrolment.

Prohibition: May not be counted with MATH1012, MATH 1002, MATH1902.

2 Course Aims, Learning Objectives and

2 Course Aims, Learning Objectives andGraduate Attributes

2.1 Course Aims

The objectives of the MATH1014 unit in Linear Algebra are to: introduce the concept of a vector;illustrate how vectors are used in real-life applications;introduce the basic concepts of linear algebra systems of linear equations, matrices,determinants, eigenvalues and eigenvectors;apply these concepts to some real world phenomena;improve your ability to think logically, analytically, and abstractly;enhance your problem-solving skills.

Students who successfully complete the MATH1014 course should:

know how to represent vectors both algebraically and geometrically in R2 and R3;be able to perform operations on vectors (addition, scalar multiplation,dot and crossproducts);be able to find equations of lines and planes in R3;be able to perform arithmetic operations in Zn;understand how to use a check digit code vector;know how to solve systems of linear equations using Gaussian elimination;set up systems of linear equations to model real world situations;know how to add and multiply matrices, and be able to find inverses;be able to find a steady state vector for a Markov process;understand how Leslie matrices are used to model population growth;be able to calculate eigenvalues and eigenvectors of 2 2 and 3 3 matrices.

2.2 Learning Outcomes

After successfully completing this unit, you should:

1. demonstrate proficiency in the new skills introduced through this unit;2. communicate mathematical ideas coherently both orally and in writing;3. use a variety of mathematical techniques to solve problems;4. be able to choose an appropriate mathematical model to describe certain situations.

2.3 Graduate Attributes

Graduate Attributes are generic attributes that encompass not only technical knowledge butadditional qualities that will equip students to be strong contributing members of professionaland social communities in their future careers. The overarching graduate attributes identifiedby the University relate to a graduates attitude or stance towards knowledge, towards the

world, and towards themselves. These are understood as a combination of five overlappingskills or abilities, the foundations of which are developed as part of specific disciplinary study.For further details please refer to the Science faculty website at:http://www.itl.usyd.edu.au/graduateAttributes/facultyGA.cfm?faculty=Science

Graduate Attributes LearningOutcomes

A Research and Inquiry

A1. Apply scientific knowledge and critical thinking to identify, define andanalyse problems, create solutions, evaluate opinions, innovate andimprove current practices.

1, 2, 3, 4

A2. Gather, evaluate and deploy information relevant to a scientific problem. 1, 2, 3, 4

A3. Design and conduct investigations, or the equivalent, and analyse andinterpret the resulting data. 1, 2, 3, 4

A4. Critically examine the truth and validity in scientific argument anddiscourse, and evaluate the relative importance of ideas. 1, 2, 3, 4

A5. Disseminate new knowledge and engage in debate around scientificissues. 1, 2, 3, 4

A6. Value the importance of continual growth in knowledge and skills, andrecognise the rapid, and sometimes major, changes in scientificknowledge and technology.

1, 2, 3, 4

B Information Literacy

B1. Use a range of searching tools (such as catalogues and databases)effectively and efficiently to find information. 1, 2, 3, 4

B2. Access a range of information sources in the science disciplines, forexample books, reports, research articles, patents and companystandards.

1, 2, 3, 4

B3. Critically evaluate the reliability and relevance of information in ascientific context. 1, 2, 3, 4

B4. Consider the economic, legal, social, ethical and cultural issues in thegathering and use of information. 1, 2, 3, 4

B5. Use information technology to gather, process, and disseminate scientificinformation. 1, 2, 3, 4

C Communication

C1. Explain and present ideas to different groups of people in plain English. 1, 2, 3, 4

C2. Write and speak effectively in a range of contexts and for a variety ofdifferent audiences and purposes. 1, 2, 3, 4

C3. Use symbolic and non-verbal communication, such as pictures, icons andsymbols as well as body language and facial expressions, effectively. 1, 2, 3, 4

C4. Present and interpret data or other scientific information using graphs,tables, figures and symbols. 1, 2, 3, 4

C5. Work as a member of a team, and take individual responsibility within thegroup for developing and achieving group goals. 1, 2, 3, 4

C6. Take a leadership role in successfully influencing the activities of a grouptowards a common goal. 1, 2, 3, 4

C7. Actively seek, identify, and collaborate with others in a professional andsocial context. 1, 2, 3, 4

D Ethical, Social and Professional Understanding

D1. Demonstrate an understanding of the significance and scope of ethicalprinciples, both as a professional scientist and in the broader socialcontext, and a commitment to apply these principles when makingdecisions.

1, 2, 3, 4

D2. Appreciate the importance of sustainability and the impact of sciencewithin the broader economic, environmental and socio-cultural context. 1, 2, 3, 4

D3. Demonstrate empathy with, and sensitivity towards, another's situation,feelings and motivation. 1, 2, 3, 4

E Personal and Intellectual Autonomy

E1. Evaluate personal performance and development, recognise gaps inknowledge and acquire new knowledge independently. 1, 2, 3, 4

E2. Demonstrate flexibility in adapting to new situations and dealing withuncertainty. 1, 2, 3, 4

E3. Reflect on personal experiences, and consider their effect on personalactions and professional practice. 1, 2, 3, 4

E4. Set achievable and realistic goals and monitor and evaluate progresstowards these goals. 1, 2, 3, 4

E5. Demonstrate openness and curiosity when applying scientificunderstanding in a wider context. 1, 2, 3, 4

2.4 Threshold Learning Outcomes

The Threshold Learning Outcomes (LTOs) are the set of knowledge, skills and competenciesthat a person has acquired and is able to demonstrate after the completion of a bachelor degreeprogram. The TLOs are not equally weighted across the degree program and the numberingdoes not imply a hierarchical order of importance.

Threshold Learning Outcomes LearningOutcomes

1 Understanding science

1.1 Articulating the methods of science and explaining why current scientificknowledge is both contestable and testable by further inquiry 1, 2, 3, 4

1.2 Explaining the role and relevance of science in society 1, 2, 3, 4

2 Scientific knowledge

2.1 Demonstrating well-developed knowledge in at least one disciplinary area 1, 2, 3, 4

2.2 Demonstrating knowledge in at least one other disciplinary area 1, 2, 3, 4

3 Inquiry and problem solving

3.1 Gathering, synthesising and critically evaluating information from a rangeof sources 1, 2, 3, 4

3.2 Designing and planning an investigation 1, 2, 3, 4

3.3 Selecting and applying practical and/or theoretical techniques or tools inorder to conduct an investigation 1, 2, 3, 4

3.4 Collecting, accurately recording, interpreting and drawing conclusionsfrom scientific data 1, 2, 3, 4

4 Communication

4.1 Communicating scientific results, information or arguments, to a range ofaudiences, for a range of purposes, and using a variety of modes 1, 2, 3, 4

5 Personal and professional responsibility

5.1 Being independent and self-directed learners 1, 2, 3, 4

5.2 Working effectively, responsibly and safely in an individual or teamcontext 1, 2, 3, 4

5.3 Demonstrating knowledge of the regulatory frameworks relevant to theirdisciplinary area and personally practising ethical conduct 1, 2, 3, 4

For further details on course learning outcomes related to specific topics see LMS site andCourse Handbook.

3 Study Commitment

The current standard work load for a 3 credit point unit of study is 3 hours per week offace-to-face teaching contact hours (2 lectures and 1 tutorial) and an additional 3 hours perweek of student independent study. Below is a breakdown of our expectations for this unit. Itshould be noted that Independent Study is based on what we believe to be the amount of timea typical student should spend to pass an item of assessment. Times are a guide only.

In class activities Hours

Lectures (26 @ 1 hr each) 26

Tutorials(12 @ 1 hr each) 12

Total 38

Independent Study Hours

Preparation for lectures (26 @ 0.5 hr each) 13

Review and self assessment (12 weeks@ 1 hr each) 12

Preparation for tutorials (12 @ 1 hr each) 12

Total 37

Study Tips

You are now in control of your own study strategy, and as an adult learner it is up to you todevise a study plan that best suits you. Many resources are available to assist your learning,including a set of independent study exercises for you to complete.

Any questions?

Before you contact us with any enquiry, please check the FAQ page at http://www.maths.usyd.edu.au/u/UG/JM/FAQ.html

Where to go for help

For administrative matters, go to the Mathematics Student Office, Carslaw room 520.For help with mathematics, see your lecturer, or your tutor. Lecturers guarantee to be availableduring their indicated office hour.If you are having difficulties with mathematics due to insufficient background, you should goto the Mathematics Learning Centre (Carslaw room 441).

4 Learning and Teaching Activities

WEEKLY SCHEDULE

LECTURES

There are two different lecture streams. You should attend one stream (that is, two lectures perweek) as shown on your personal timetable. Lectures run for 13 weeks and the last lecture willbe on Tuesday 25 October.

Times Location Lecturer

10am Mon & Tue EAve Auditorium to be advised

11am Mon &

11 am Tue

Chem LT 3

General LTto be advised

Consultation times

Lecturers are available for consultation as follows:

When Where (Weeks 1-6) Where (Weeks 7-13)

to be advised to be advised to be advised

to be advised to be advised to be advised

TUTORIALS

One tutorial per week, starting in week 1. You should attend the tutorial given on yourpersonal timetable. Attendance at tutorials will be recorded. Your attendance will not berecorded unless you attend the tutorial in which you are enrolled.

Tutorial sheets

The tutorial sheets for a given week will be available on the MATH1014 webpage by theFriday of the previous week. You must take the current weeks sheet to your tutorial. Thesheet must be printed from the web.Tutorial exercises may include exercises from the textbook. When that is the case, you willneed to take your textbook (or a copy of the relevant pages) to the tutorial with you.

WEEK-BY-WEEK OUTLINE

Week Topics Text reference

1 Geometry and algebra of vectors Section 1.1, pp 312

2 Length, dot product, cross product Section 1.2, pp 1523Exploration, pp 45,463 Lines and planes Section 1.3, pp 31384 Code vectors and modular arithmetic Section 1.4, pp 4755

5 Systems of linear equations; elementary row operations Sections 2.1, 2.2, pp 6073

6 Gaussian and Gauss-Jordan Elimination; applicationsSection 2.2, pp 7381Section 2.4, pp 102114

7 Matrices Section 3.1, pp 137151Section 3.2, p 153, pp 1571608 The inverse of a matrix Section 3.3, pp 162168

9 Markov chains Leslie population modelsSection 3.7, pp 229234Section 3.7, pp 234236

10Introduction to eigenvalues andeigenvectors (one lecture only)

Section 4.1, pp 254259

11 Determinants Section 4.2, pp 263266,269274

12 Eigenvalues and eigenvectors Section 4.3, pp 290293Section 4.6, pp 32833013 Revision

5 Teaching Staff and Contact Details

Unit Coordinator Email

Dr DavidEasdown david.easdown@sydney.edu.au

Teaching Staff Email Room Phone Note

to be advised to be advised to be advised

6 Learning Resources

Textbook

Poole D. Linear Algebra: A Modern Introduction. Brooks/Cole, USA.

Available from the Co-op Bookshop.

References

Anton H and R Busby, 2003. Contemporary Linear Algebra. Wiley, USA.Lay D, 2005. Linear Algebra and its Applications. 3rd Edition. Pearson, USA.Poole D, 2010. Linear Algebra: A Modern Introduction. 3rd Edition. Cengage Learning, USA.Strang G, 2005. Linear Algebra and its Applications. 4th Edition. Brooks/Cole, USA.

Web Site

It is important that you check the Junior Mathematics web site regularly.It may be found through Blackboard, by following links from the University of Sydney frontpage, or by going directly to http://www.maths.usyd.edu.au/u/UG/JM/

Important announcements relating to Junior Mathematics are posted on the site, and there is alink to the MATH1014 page. Material available from the MATH1014 page may includeinformation sheets, the Junior Mathematics Handbook, notes, exercise sheets and solutions,and previous examination papers.

7 Assessment Tasks

You are responsible for understanding the University policy regarding assessment andexamination.

Formative and Summative Assessment

Assessment in this unit will be both formative (for feedback) and summative (for marks). Quizzes and assignments incorporate both formative and summative assessment. Formativeassessment provides feedback on your performance, and summative assessment comprisesmarks for performance in assignments, quizzes and examinations, which will count towards afinal unit mark.

7.1 Summative Assessments

Assessment Task Percentage Mark Due Date Learning Outcomes

Quiz 1 15 Week 5 (week starting Sunday, 24 August 2014)

1, 2, 3, 4

Quiz 2 15 Week 11 (week starting Sunday, 12 October 2014)

1, 2, 3, 4

Assignment 5 Week 8 (week starting Sunday, 14 September 2014)

1, 2, 3, 4

Final exam 65 Exam Period 1, 2, 3, 4

Descriptions of Summative Assessments

Quiz 1

Quiz 2

Assignment

Final exam

7.2 Assessment Grading

Your final raw mark for this unit will be calculated as follows:

Exam at end of semester: 65%

Quiz 1 mark (using the bettermark principle): 15%Quiz 2 mark (using the bettermark principle): 15%Assignment mark: 5%

The bettermark principle means that for each quiz, the quiz counts if and only if it isbetter than or equal to your exam mark. If your quiz mark is less than your exam markthe exam mark will be used for that portion of your assessment instead. So forexample if your quiz 1 mark is better than your exam mark while your quiz 2 mark isworse than your exam mark then the exam will count for 80%, quiz 1 will count for15% and the assignment will count for 5% of your overall mark. The assignment markcounts for 5% regardless of whether it is better than your exam mark or not. Final grades are returned within one of the following bands:

High Distinction (HD), 85100: representing complete or close to completemastery of the material;Distinction (D), 7584: representing excellence, but substantially less thancomplete mastery;Credit (CR), 6574: representing a creditable performance that goes beyondroutine knowledge and understanding, but less than excellence;Pass (P), 5064: representing at least routine knowledge and understandingover a spectrum of topics and important ideas and concepts in the course.

A student with a passing or higher grade should be well prepared to undertake furtherstudies in math- ematics on which this unit of study depends.

8 Learning and Teaching Policies

For full details of applicable university policies and procedures, see the Policies Online siteat https://sydney.edu.au/policy

Academic Policies relevant to student assessment, progression and coursework:

Academic Dishonesty in Coursework. All students must submit a cover sheet for allassessment work that declares that the work is original and not plagiarised from thework of others. The University regards plagiarism as a form of academic misconduct,and has very strict rules that all students must adhere to. For information see thedocument defining academic honesty and plagiarism at:

https://sydney.edu.au/policies/showdoc.aspx?recnum=PDOC2012/254&RendNum=0

Coursework assessment policy. For information, see the documents outlining theUniversity assessment policy and procedures at:

https://sydney.edu.au/policies/showdoc.aspx?recnum=PDOC2012/266&RendNum=0 andhttps://sydney.edu.au/policies/showdoc.aspx?recnum=PDOC2012/267&RendNum=0.

The Faculty process is to use standards based assessment for units where grades arereturned and criteria based assessment for Pass / Fail only units. Norm referencedassessment will only be used in exceptional circumstances and its use will need to bejustified to the Undergraduate Studies Committee. Special consideration for illness ormisadventure may be considered when an assessment component is severelyaffected. Details of the information that is required to be submitted along with theappropriate procedures and forms is available at:

https://sydney.edu.au/science/cstudent/ug/forms.shtml#special_consideration

Start by going to the Faculty of Science Webpage, and downloading the SpecialConsideration pack at the link above.

Special Arrangements for Examination and Assessment. In exceptionalcircumstances alternate arrangements for exams or assessment can be made. Howeverconcessions for outside work arrangements, holidays and travel, sporting andentertainment events will not normally be given. The policy, guidelines and applicationform including examples of circumstances under which you might be awarded a specialarrangement for an examination or assessment task can be found at:

https://sydney.edu.au/science/cstudent/ug/forms.shtml#special_arrangements

Student Appeals against Academic Decisions. Students have the right to appeal anyacademic decision made by a school or the faculty. The appeal must follow theappropriate procedure so that a fair hearing is obtained. The formal application form canbe obtained at:

https://sydney.edu.au/science/cstudent/ug/forms.shtml#appeals

Relevant forms are available on the Faculty policies websiteat https://sydney.edu.au/science/cstudent/ug/forms.shtml

Special consideration and special arrangements

Students who suffer serious illness or misadventure that may affect their academicperformance may request that they be given special consideration in relation to thedetermination of their results.Students who are experiencing difficulty in meeting assessment tasks due to competingessential community commitments may request that special arrangements be made in respectof any or all factors contributing to their assessment.The Faculty of Science policies on these issues apply to all Mathematics and Statistics units ofstudy. Information relating to these policies, including the Application Packs and instructionson how to apply, can be obtained from the Faculty of Science website.Before applying for special consideration, please read the Faculty Policy, and the rest of thissection, to determine whether or not you are eligible. Note that occasional brief or trivialillness will not generally warrant special consideration.

How to apply

Applications for special Consideration must be made within 5 working days of the date forwhich consideration is being sought.Applications for special arrangements must be submitted at least seven days BEFORE the duedate of the assessment or examination for which alternative arrangements are being sought.

The procedure is as follows.

Obtain the application forms from the Faculty of Science website or from the StudentInformation Office of the Faculty of Science.Take the original paperwork, plus one copy for each piece of assessment for whichconsideration is being sought, to the Student Information Office of the Faculty ofScience. Note that applications are to be lodged with the Science Faculty, regardless ofthe faculty in which you are enrolled. Your copies will be stamped at the Faculty StudentInformation Office.Take the stamped documentation to the Mathematics Student Services Office, Carslawroom 520 opposite the lifts on Carslaw Level 5). Your personal information must becompleted on all the forms, including the Academic Judgement form, before the formwill be accepted.

Note that an application for special consideration or special arrangements is a request only,and not a guarantee that special consideration will be granted or special arrangements made.Applications are considered in the light of your participation in the unit during the semester,and your academic record in mathematics.

Special consideration relating to assignments

Applications for special consideration relating to assignments will not be accepted.Exemptions from submission of assignments are not generally granted. If serious illness ormisadventure during the period prior to the due date prevents you from submitting anassignment on the due date then you should do the following:

Contact the Mathematics Student Office (by phone or email, or in person) to request anextension. Unless there are exceptional circumstances you must do this before the duedate.

1.

If you are granted an extension, take your assignment to the Mathematics Student Officeby the extended due date. (Do not put the assignment in the collection boxes.)

2.

Submit some supporting documentation (for example, a medical certificate) when youhand in your assignment.

3.

Late assignments will only be accepted if you have an approved extension, or in the followingcircumstance:Should you be ill on the due date only, and unable to submit your assignment, then you maysubmit it the following day, accompanied by supporting documentation (for example, amedical certificate). In this case, your assignment should be taken to Mathematics StudentOffice. (Do not put the assignment in the collection boxes.)

Special consideration relating to quizzes

If you miss a quiz due to illness or misadventure, then you must go to the Mathematics StudentServices Office as soon as possible afterwards. Arrangements may be made for you to sit thequiz at another time. If that is not possible then you may be eligible to apply for specialonsideration.If your application for special consideration relating to missing a quiz is successful then apro-rata mark for that quiz will be awarded, based on your final examination mark in the unitof study.

Special consideration relating to end-of-semester examinations

If you believe that your performance on an exam was impaired due to illness or misadventureduring the week preceding the exam, then you should apply for 28 special consideration. Ifyour application is successful then your mark may be adjusted, or you may be offered theopportunity to sit a supplementary exam.Please note that illness or misadventure during the week preceding the exam is not anacceptable reason for missing an exam. If you miss an exam due to illness or misadventure onthe day of the exam then you should apply for special consideration. If your application issuccessful you will be granted the opportunity to sit a supplementary examination.Students who have participated only minimally in the unit throughout the semester will not begranted supplementary exams.

Special consideration relating to attendance

The Faculty policy applies. Note that special consideration will not be granted for brief illnessor minor misadventure that causes you to miss a tutorial. Unless a quiz was held during thetutorial, applications for special consideration in such cases will not be accepted. Jury duty, military service, national sporting and religious or cultural commitments

Students who will miss an assessment due to commitments such as these may apply for specialarrangements to be made. The Faculty of Science Special Arrangements Policy applies for allfirst year mathematics units. Note that an application for special arrangements must be madeat least seven days before the date of the assessment concerned.

Replacement assessments for end of semester examinations

Students who apply for and are granted either special arrangements or special consideration forend of semester examinations in units offered by the Faculty of Science will be expected to sitany replacement assessments in the two weeks immediately following the end of the formalexamination period. Later dates for replacement assessments may be considered where theapplication is supported by appropriate documentation and provided that adequate resourcesare available to accommodate any later date.

are available to accommodate any later date.