Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title Maths and Statistics for Data Science and AI
Code CSCK544
Coordinator Professor FP Coenen
Computer Science
Coenen@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2021-22 Level 7 FHEQ Whole Session 15

Aims

1. To provide students with a systematic understanding of the key mathematical and statistical concepts and techniques underpinning established mechanisms of Data Science and AI.
2. To provide students with sufficient mathematical and statistical knowledge to understand the operation and deployment of key tools and techniques of Data Science and AI.
3. To provide students with an appropriate level of knowledge to able to interpret the results generated when using the techniques of Data Science and AI.


Learning Outcomes

(M1) A systematic understanding of basic mathematical principles and methods of interest to Data Science and AI.

(M2) A critical awareness of basic and more specialised concepts in probability theory and statistics relevant to Data Science and AI.

(M3) An ability to undertake software projects in the domain of Data Science and AI.

(M4) An ability to communicate the outcomes of experimental work in the domain of Data Science and AI.

(S1) Communication skills in electronic as well as written form.

(S2) Self-direction and originality in tackling and solving problems within the domain of Computer Science, and an ability to act autonomously in planning and implementing solutions in a professional manner.

(S3) An ability to act autonomously and professionally when planning and implementing solutions to computer science problems.

(S4) Experience of working in development teams, respecting others, co-operating, negotiating/persuading, awareness of interdependence with others.

(S5) Group working, respecting others, co-operating, negotiating/persuading, awareness of interdependence with others


Syllabus

 

Weeks 1 and 2: Differential Calculus
Review of basic calculus - numbers, sets and functions. Basic geometry, coordinate systems, lines and trigonometry. Limits, continuity, derivatives, velocity, concavity in differential calculus.
Optimisation -minima/maxima, gradient descent and second order methods (Newton)

Weeks 3 and 4: Linear Algebra
Basic concepts - vectors, matrices, dot products and matrix product. Geometry of matrices and derivatives, linear transformations and partial derivatives. Extensions - Eigen values and vectors, determinants. Linear basis and projections, Eigen-decomposition and SVD, pseudoinverse.

Weeks 5 and 6: Probability Theory
Basic probability - events, sample space, frequentist vs Bayesian approach, law of large numbers, conditional probability, independence, Bayes theorem and random variables. Probability distributions - probability sampling, random sampling and sampling distributions.

Weeks 7 and 8: Statistics
Measures of centre and variation, statistical significance (confidence intervals) and hypothesis testing. Errors, chi-square independence test, Correlation vs causation. Descriptive statistic. Data presentation: scatter plots, line graphs, bar charts, histograms and box plots.


Teaching and Learning Strategies

The mode of delivery is by online learning, facilitated by a Virtual Learning Environment (VLE). This mode of study enables students to pursue modules via home study while continuing in employment. Module delivery involves the establishment of a virtual classroom in which a relatively small group of students (usually 10-25) work under the direction of a faculty member. Module delivery proceeds via a series of eight one-week online sessions, each of which comprises an online lecture, supported by other eLearning activities, posted electronically to a public folder in the virtual classroom. The mode of learning includes a range of required and optional eLearning activities, including but not limited to: lecture casts, live seminars, self-assessment opportunities, and required and suggested further reading and try-for-yourself activities. Communication within the virtual classroom is asynchronous, preserving the requirement that students are able to pursue the module in their own time, within the weekly time-frame of each online session. An important element of the module provision is active learning through collaborative, cohort-based, learning using discussion fora where the students engage in assessed discussions facilitated by the faculty member responsible for the module. This in turn encourages both confidence and global citizenship (given the international nature of the online student body).


Teaching Schedule

  Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
Study Hours 24

        40

64
Timetable (if known)              
Private Study 86
TOTAL HOURS 150

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
             
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Practical Assessment 2. Practical exercise directed at probability theory and statistics  1500-2250 words    30       
Practical Assessment 1. Practical exercise directed at differential Calculus and linear algebra.  1500-2250 words    30       
Discussion Question 2: Use the online discussion forum to critically discuss experiences and opinion within the cohort relating to some aspect of maths and statistics in Data Science and AI .  1000-1500 words    20       
Discussion Question 1: Use the online discussion forum to critically discuss experiences and opinion within the cohort relating to some aspect of maths and statistics in Data Science and AI .  1000-1500 words    20       

Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.