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MATHS 7027 - Mathematical Foundations of Data Science

North Terrace Campus - Semester 1 - 2021

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 1
    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.
    Assessment Exam, ongoing assessment
    Course Staff

    Course Coordinator: Dr Stuart Johnson

    Course Timetable

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

  • 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)
    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
  • 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 (online) lectures and computer laboratories 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.
    Workload

    No information currently available.

    Learning Activities Summary
    Fundamentals (weeks 1-3)
     - Approximation
     - Functions
     - Summation 
     - Series Approximation
     - InductionLinear

    Algebra (weeks 4-7)
     -
    Vectors and matrices 
     - Systems of linear equations 
     - Eigenvalues and eigenvectors
      - Dimension reduction 

    Probability (weeks 8-9) 
     - Counting 
     - Discrete random variables 
     - Conditional probability 
     - Bayes theorem 

    Calculus (weeks 10-12) 
     - 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
    Assignments 25%
    Quizzes 10%
    Tutorials & Computer Participation 5%
    Test 1 15%
    Test 2 15%
    Exam 30%
    Assessment Related Requirements
    An aggregate score of 50% is required to pass the course.
    Assessment Detail
    Written assignments are due every fortnight, the first is due in Week 3.

    Computer Exercises are fortnightly beginning in Week 1.

    Tutorials are fortnightly beginning in Week 2.

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

    No information currently available.

    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 .

  • 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鈥檚 disciplinary procedures.

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