MATHS 7027 - Mathematical Foundations of Data Science

North Terrace Campus - Trimester 2 - 2022

This course introduces fundamental mathematical concepts relevant to computer science and provides a basis for further postgraduate study in data science, statistical machine learning, and cybersecurity. Topics covered are probability: sets, counting, probability axioms, Bayes theorem; optimisation and calculus: differentiation, integration, functions of several variables, series approximations; linear algebra: vector and matrices, matrix algebra, vector spaces; discrete mathematics and statistics: linear regression, linear least squares, regularisation. Applications of the theory to data science and machine learning will be developed.

  • General Course Information
    Course Details
    Course Code MATHS 7027
    Course Mathematical Foundations of Data Science
    Coordinating Unit School of Mathematical Sciences
    Term Trimester 2
    Level Postgraduate Coursework
    Location/s North Terrace Campus
    Units 3
    Contact Up to 5 hours per week
    Available for Study Abroad and Exchange Y
    Restrictions Not available to MMaSc students.
    Course Description This course introduces fundamental mathematical concepts relevant to computer science and provides a basis for further postgraduate study in data science, statistical machine learning, and cybersecurity. Topics covered are probability: sets, counting, probability axioms, Bayes theorem; optimisation and calculus: differentiation, integration, functions of several variables, series approximations; linear algebra: vector and matrices, matrix algebra, vector spaces; discrete mathematics and statistics: linear regression, linear least squares, regularisation. Applications of the theory to data science and machine learning will be developed.
    Course Staff

    Course Coordinator: Mr Max Glonek

    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 basic mathematical concepts in data science, relating to linear algebra, probability, and calculus.
    2. Employ methods related to these concepts in a variety of data science applications.
    3. Apply logical thinking to problem-solving in context.
    4. Demonstrate skills in writing mathematics.
    University Graduate Attributes

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

    University Graduate Attribute Course Learning Outcome(s)

    Attribute 1: Deep discipline knowledge and intellectual breadth

    Graduates have comprehensive knowledge and understanding of their subject area, the ability to engage with different traditions of thought, and the ability to apply their knowledge in practice including in multi-disciplinary or multi-professional contexts.

    all

    Attribute 2: Creative and critical thinking, and problem solving

    Graduates are effective problems-solvers, able to apply critical, creative and evidence-based thinking to conceive innovative responses to future challenges.

    3,4

    Attribute 3: Teamwork and communication skills

    Graduates convey ideas and information effectively to a range of audiences for a variety of purposes and contribute in a positive and collaborative manner to achieving common goals.

    4

    Attribute 4: Professionalism and leadership readiness

    Graduates engage in professional behaviour and have the potential to be entrepreneurial and take leadership roles in their chosen occupations or careers and communities.

    2

    Attribute 7: Digital capabilities

    Graduates are well prepared for living, learning and working in a digital society.

    1,2

    Attribute 8: Self-awareness and emotional intelligence

    Graduates are self-aware and reflective; they are flexible and resilient and have the capacity to accept and give constructive feedback; they act with integrity and take responsibility for their actions.

    3,4
  • Learning Resources
    Required Resources
    All required resources are provided in MyUni. There is no requirement to buy a textbook.
    Recommended Resources
    1. Lay: Linear Algebra and its Applications 4th ed. (Addison Wesley Longman)
    2. Stewart: Calculus 7th ed. (international ed.) (Brooks/Cole)
    3. Graham, Knuth, Patashnik: Concrete Mathematics (Addison-Wesley)
    4. Deisenroth, Faisal, Ong: Mathematics for Machine Learning (Cambridge University Press)
  • Learning & Teaching Activities
    Learning & Teaching Modes
    This course relies on workshops and computer exercises to guide students
    through the course material, tutorial classes to provide students with
    class/small group/indvidual assistance, and a sequence of assignments to
    provide formative assessment opportunities for students to practise
    techniques and develop their understanding of the course.
    Workload

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

    This is a 3-unit course. In the semester or trimester format, you are expected to allocate the following study time to fully meet the Course Learning Outcomes (CLOs) for this course. Please note that students work at different paces, so this indicates the approximate time required to complete this course.

    Learning Activity Hours / Week Duration Total
    Online Learning Activities 2 hours 12 weeks 24 hours
    Face to Face Learning Activities 2 hours 12 weeks 24 hours
    Independent Study 4 hours 12 weeks 24 hours
    Assessment Tasks 5 hours 12 weeks 60 hours
    Total 156 hours


    Learning Activities Summary

    Lecture Outline

    Fundamentals (weeks 1-2)
    • Approximation
    • Sets and functions
    • Sums and series
    Probability (weeks 3-4)
    • Counting
    • Discrete random variables
    • Conditional probability
    • Bayes' theorem
    Representing Data with Matrices (weeks 5-6)
    • Matrix operations
    • Matrix equations
    • Determinants
    Solving Linear Equations (weeks 7-8)
    • Row reduction
    • Applications
    • Linear independence
    Dimensionality Reduction (weeks 9-10)
    • Eigenvalues and eigenvectors
    • Dimension reduction
    Applications of Calculus (weeks 11-12)
    • Integration and continuous probability distributions
    • Series approximations
    • Gradient descent
  • 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
    Component Weighting
    Assignments 20%
    Quizzes 10%
    Test 1 10%
    Test 2 10%
    Exam 50%
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Precise details of all assessment will be provided on the MyUni site for this course.
    Submission
    All written assignments are to be e-submitted following the instructions on MyUni.

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

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

    M10 (Coursework Mark Scheme)
    Grade Mark Description
    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.

  • 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 student’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.