## MATHS 7027 - Mathematical Foundations of Data Science

### North Terrace Campus - Semester 2 - 2023

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 include: 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 Mathematical Foundations of Data Science Mathematical Sciences Semester 2 Postgraduate Coursework North Terrace Campus 3 Up to 5 hours per week Y SACE Stage 2 Mathematical Methods Not available to MMaSc students. 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 include: 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

No information currently available.

##### 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.

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

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 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.

No information currently available.

### 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

Dimensional Reduction (weeks 9-10)
- Eigenvalues and eigenvectors
- Dimension reduction

Applications of Calculus (weeks 11-12)
- Integration and continuous probability distributions
- Series Approximations
• 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.

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.

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.

• 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.

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