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.

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.)

1. Poole, D., Linear Algebra: a Modern Introduction 4th edition (Cengage Learning)
2. Stewart, J., Calculus 8th 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 may be purchased from the Co-op bookshop on campus or from the publisher and electronic versions are also available for purchase 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.

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.

This course relies on lectures 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 practice techniques and develop their understanding of the course.

For additional support we also run a drop-in service called First Year Maths Help on the ground floor of Ingkarni Wardli. This is staffed with tutors Monday to Friday 10am-4pm. Just drop in whenever!

Activity	Quantity	Workload hours
Lectures	48	84
Tutorials	11	11
Assignments and practice	11	55
Mid Semester Test	1	6
Total		156

In Mathematics IA the two topics of algebra and calculus detailed below are taught in parallel, with two lectures a week on each. The tutorials are a combination of algebra and calculus topics, pertaining to the previous week's lectures.

Lecture Outline

Algebra

• Linear systems and Gauss-Jordan elimination (5 lectures)
  • 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 (4 lectures)
  • Linear combinations of vectors
  • Homogeneous linear systems
  • Linearly independent sets of vectors
  • Subspaces and bases
• Matrix algebra (5 lectures)
  • Addition of matrices
  • Multiplication of matrices
  • Applications
  • Elementary matrices
  • The inverse of a matrix
• Optimisation (6 lectures)
  • Introduction, definitions
  • Convex sets and vertices
  • The method of slack variables
• Determinants (3 lectures)
  • Definition of the determinant
  • Determinants and elementary row operations

Calculus

• Functions (5 lectures)
  • Definition, domain and range. Examples of functions.
  • Inverses, inverse trigonometric functions.
  • Zeros of functions.
  • Limits, continuity.
  • Interval bisection method.
• Differentiation and its applications (7 lectures)
  • Definition, interpretation, concavity.
  • Rules for differentiation (product, quotient, chain).
  • Implicit differentiation, derivatives of inverses.
  • Related rates.
  • Maxima and minima of functions and applications
• Integration (10 lectures)
  • Summation notation, definition of definite integral.
  • Antiderivatives and The Fundamental Theorem of Calculus.
  • Techniques of integration: substitution, parts, partial fractions.
  • Applications.
  • Improper integrals.

Assessment Task	Task Type	Weighting	Learning Outcomes
Written Assignments	Formative	7.5%	all
MapleTA Assignments	Formative	7.5%	all
Tutorial Participation	Formative	5%	all
Mid Semester Test	Summative and Formative	10%	1,2,3,4
Exam	Summative	70%	1,2,3,4,5,6

Due to the current COVID-19 situation modified arrangements have been made to assessments to facilitate remote learning and teaching. Assessment details provided here reflect recent updates.

Assignments - 35% weighting
Mid Semester Test - 15% weighting
Final Examination - 50% weighting

The modified assessment weightings for Maths IA are as follows:

Assignments (both Written and Mobius) continue as before. Note that for Written and Mobius 1, 2 and 3, either the original weighting or the amended weighting will be applied, whichever gives you the higher overall assignment mark at the end of semester.

The Mid Semester Test will take place in one of the lecture times in Week 7, Monday 27th April - Friday 1st of May. The Test will be
conducted online via Mobius. Further details about the test will be provided closer to the date.

The final Examination will take place in the usual exam period at the end of semester. This exam will be administered online via MyUni. Further details about the exam will be provided closer to the date.

An aggregate score of 50% is required to pass the course. Furthermore students must achieve at least 45% on the final examination to pass the course.

Written assignments are due every fortnight, the first is released in Week 1 and due in Week 3.

Maple TA (online) assignments are due every week, the first is released in Week 1 and due in Week 3.

Tutorials are weekly beginning in Week 2.

The Mid Semester Test occurs in your enrolled computer lab in Week 6.

Precise details of all of these will be provided on the MyUni site for this course.

1. All written assignments are to be e-submitted following the instructions on MyUni.
2. Late assignments will not be accepted without a medical certificate.
3. Written assignments will have a one week turn-around time for feedback to students.
4. Online Maple TA assignments provide instantaneous feedback to students.

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

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:

https://www.adelaide.edu.au/student/exams/modified-arrangements-for-coursework-assessment/replacement-examinations-and-additional-assessment