## MATHS 1011 - Mathematics IA

### North Terrace Campus - Semester 2 - 2021

This course, together with MATHS 1012 Mathematics IB, provides an introduction to the basic concepts and techniques of calculus and linear algebra, emphasising their inter-relationships and applications to engineering, the sciences and financial areas, introduces students to the use of computers in mathematics, and develops problem solving skills with both theoretical and practical problems. Topics covered are - Calculus: Functions of one variable, differentiation and its applications, the definite integral, techniques of integration. Algebra: Systems of linear equations, subspaces, matrices, optimisation, determinants, applications of linear algebra.

• General Course Information
##### Course Details
Course Code MATHS 1011 Mathematics IA Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 5 hours per week Y At least a C- in both SACE Stage 2 Mathematical Methods (formerly Mathematical Studies) and SACE Stage 2 Specialist Mathematics; or a 3 in International Baccalaureate Mathematics HL; or MATHS 1013. ECON 1005, ECON 1010, MATHS 1009, MATHS 1010 At least B in both SACE Stage 2 Mathematical Methods (formerly Mathematical Studies) and SACE Stage 2 Specialist Mathematics. Students who have not achieved this standard are strongly advised to take MATHS 1013 before attempting MATHS 1011. Ongoing assessment, exam

##### Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
##### Course Learning Outcomes
On successful completion of this course students will be able to:
1. Demonstrate understanding of and proficiency with basic concepts in linear algebra: systems of linear equations, subspaces, matrices, optimisation, determinants.
2. Demonstrate understanding of and proficiency with basic concepts in calculus: functions of one variable, differentiation and its applications, the definite integral, techniques of integration.
3. Employ methods related to these concepts in a variety of applications.
4. Apply logical thinking to problem-solving in context.
5. Demonstrate an understanding of the role of proof in mathematics.
6. Demonstrate skills in writing mathematics.

This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

University Graduate Attribute Course Learning Outcome(s)
Deep discipline knowledge
• informed and infused by cutting edge research, scaffolded throughout their program of studies
• acquired from personal interaction with research active educators, from year 1
• accredited or validated against national or international standards (for relevant programs)
all
Critical thinking and problem solving
• steeped in research methods and rigor
• based on empirical evidence and the scientific approach to knowledge development
• demonstrated through appropriate and relevant assessment
3,4,5
• Learning Resources
##### Required Resources
A comprehensive set of Course Notes will be available as a PDF on the MyUni site for this course. (More specific details will be provided on MyUni.)
##### Recommended Resources
1. Poole, D., Linear Algebra: a Modern Introduction 4th edition (Cengage Learning)
2. Stewart, J., Calculus 9th edition (metric version) (Cengage Learning)
While it is not compulsory to buy the texts, they are recommended, especially for students who want extra support in this course. Copies of these text books (hardcopy or electronic) may be purchased from the publisher. Copies of both books are available in the Barr Smith Library for short term borrowing and reference. These are also the textbooks for MATHS 1012 Mathematics IB.
##### Online Learning

This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes and videos, assignment and tutorial questions, and worked solutions. Students should make appropriate use of these resources. MyUni can be accessed here: https://myuni.adelaide.edu.au/

This course also makes use of online assessment software for mathematics called Mobius, which we use to provide students with instantaneous formative feedback. Further details about using Mobius will be provided on MyUni.

Students are also reminded that they need to check their University email on a daily basis. Sometimes important and time-critical information might be sent by email and students are expected to have read it. Any problems with accessing or managing student email accounts should be directed to Technology Services.

• Learning & Teaching Activities
##### Learning & Teaching Modes
This course relies on lecture videos to guide students through the material, tutorial classes to provide students with small group and individual assistance, and a sequence of written and online assignments to provide formative assessment opportunities for students to practise techniques and develop their understanding of the course.

We provide additional support via discussions on MyUni and via "drop-in" help.

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

 Activity Quantity Workload hours Course Notes & Videos 1 set 72 Lectures 12 12 Tutorials 11 11 Assignments & Practice 11 55 Mid Semester Test 1 6 Total 156
##### Learning Activities Summary
In Mathematics IA the two topics of algebra and calculus detailed below are taught in parallel. The tutorials are a combination of algebra and calculus topics, pertaining to the previous week's lectures.

Topic Outline

Algebra

• Linear systems and Gauss-Jordan elimination
• Systems of linear equations and elementary operations
• Reduced row echelon form
• The three possible outcomes of Gauss-Jordan elimination
• Applications
• Spanning sets and linearly independent sets
• Linear combinations of vectors
• Homogeneous linear systems
• Linearly independent sets of vectors
• Subspaces and bases
• Matrix algebra
• Multiplication of matrices
• Applications
• Elementary matrices
• The inverse of a matrix
• Optimisation
• Introduction, definitions
• Convex sets and vertices
• The method of slack variables
• Determinants
• Definition of the determinant
• Determinants and elementary row operations

Calculus

• Functions
• Definition, domain and range. Examples of functions.
• Inverses, inverse trigonometric functions.
• Zeros of functions.
• Limits, continuity.
• Interval bisection method.
• Differentiation and its applications
• Definition, interpretation, concavity.
• Rules for differentiation (product, quotient, chain).
• Implicit differentiation, derivatives of inverses.
• Related rates.
• Maxima and minima of functions and applications
• Integration
• Summation notation, definition of definite integral.
• Antiderivatives and The Fundamental Theorem of Calculus.
• Techniques of integration: substitution, parts, partial fractions.
• Applications.
• Improper integrals.
• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

##### Assessment Summary
 Assessment Task Task Type Weighting Learning Outcomes Written Assignments Formative and Summative 12.5% all Mobius Assignments Formative and Summative 12.5% all Mid Semester Test Summative and Formative 15% 1,2,3,4 Final Exam Summative 60% 1,2,3,4,5,6
##### Assessment Related Requirements
An aggregate score of 50% is required to pass the course.
##### Assessment Detail

Precise details of the nature and timing of all assessment components will be provided on the MyUni site for this course.

##### Submission
See MyUni for more comprehensive details regarding assignment submission, our late policy etc.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
FNS   Fail No Submission
F 1-49 Fail
P 50-64 Pass
C 65-74 Credit
D 75-84 Distinction
HD 85-100 High Distinction
CN   Continuing
NFE   No Formal Examination
RP   Result Pending

Further details of the grades/results can be obtained from Examinations.

Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

Final results for this course will be made available through Access Adelaide.

Replacement and Additional Assessment Examinations (R/AA Exams)

Students are encouraged to read the University's R/AA exam information on the University’s Examinations webpage here:

• Student Feedback

The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

• Student Support
• Policies & Guidelines
• Fraud Awareness

Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's studentâ€™s disciplinary procedures.

The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.

```
```