MATHS 7027 - Mathematical Foundations of Data Science

North Terrace Campus - Semester 2 - 2019

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 Mathematical Sciences
    Term Semester 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
    Assessment Exam, ongoing assessment
    Course Staff

    Course Coordinator: Professor Lewis Mitchell

    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)
    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)
    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
  • Learning Resources
    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 lectures to guide students through the material, tutorial classes to provide students with class/small group/individual assistance,and a sequence of assignments to provide formative assessment opportunities for students to practise techniques and develop their understanding of the course.

    No information currently available.

    Learning Activities Summary

    Lecture Outline

    Fundamentals (12 Lectures)

    • Approximation
    • Functions
    • Summation
    • Series Approximation
    • Induction

    Linear Algebra (16 Lectures)

    • Vectors and matrices
    • Systems of linear equations
    • Eigenvalues and eigenvectors
    • Dimension reduction
    • The relationship between linear algebra and statistical regression

    Probability (8 Lectures)

    • Counting
    • Discrete random variables
    • Conditional probability
    • Bayes theorem

    Calculus (12 Lectures)

    • Differential calculus for optimisation
    • Integration and continuous probability distributions
    • 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
    Written Assignments: 20% total (5 x 4% each)
    Tutorial & Workshop Participation: 10% total (11 x weekly workshop written quizzes + 6 x tutorials) 
    Final Exam: 70% total
    Assessment Related Requirements
    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.
    Assessment Detail
    Written assignments are due every fortnight, the first is due in Week 3.

    Workshops (including a short written quiz) will be weekly, starting in Week 2.

    Tutorials are fortnightly beginning in Week 2.

    Precise details of all of these will be provided on the MyUni site for this course.
    All written assignments are to be e-submitted following the instructions on MyUni.

    Late assignments will not be accepted without a medical certificate.

    Written assignments will have a one week turn-around time for feedback to students.

    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 ( 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
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