### 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 AI and Data Science Code COMP533 Coordinator Professor LA Gasieniec Computer Science L.A.Gasieniec@liverpool.ac.uk Year CATS Level Semester CATS Value Session 2021-22 Level 7 FHEQ First Semester 15

### Aims

This module aims to cover the key concepts and techniques from linear algebra,
differential calculus, probability theory and statistics. The acquired knowledge
will help the student to interpret the results generated during data analysis.

### Learning Outcomes

(LO1) Good understanding of basic mathematical principles and methods of interest to data scientists. The main focus is on differential calculus and linear algebra.

(LO2) Critical awareness of basic and more specialised concepts in probability theory and statistics relevant to data science.

(LO3) Ability to undertake a small software project in the domain of data science.

(LO4) Ability to communicate the outcome of experimental work in the domain of data science.

(S1) Problem Solving – Numeracy and computational skills.

(S2) Problem Solving – Analysing facts and situations and applying creative thinking to develop appropriate solutions.

### Syllabus

DIFFERENTIAL CALCULUS (3 weeks)
- Review of basic calculus: numbers, sets, functions, limits,
- basic geometry: coordinates, lines, trigonometry
- Differential calculus: limits, continuity, derivatives, velocity, concavity
- Optimisation: minima/maxima, gradient descent, second order methods (Newton)

LINEAR ALGEBRA (3 weeks)
- Basic concepts: vectors, matrices, dot products, matrix product
- Geometry of matrices and derivatives, linear transformations and partial derivatives
- Extensions: eigen values and vectors, determinants
linear basis and projections, eigen-decomposition & SVD, pseudoinverse.

PROBABILITY THEORY (3 weeks)
- Basic probability: events, sample space, frequentist vs Bayesian approach,
law of large numbers, conditional probability, independence, Bayes theorem,
random variables
- Probability distributions, probability sampling, random sa mpling, sampling distributions

STATISTICS (3 weeks)
Measures of Centre and Variation,
Statistical Significance (Confidence intervals) and Tests of Hypothesis
- errors, chi-square independence test,
Correlation vs causation, Linear Regression
Descriptive Statistics: Data and Data Presentation: scatter plots, line graphs, bar charts, histograms, box plots

### Teaching and Learning Strategies

Teaching Method 1 - Lecture
Description:
Attendance Recorded: Not yet decided

Teaching Method 2 - Tutorial
Description:
Attendance Recorded: Not yet decided

Due to Covid-19, in 2021/22, one or more of the following delivery methods will be implemented based on the current local conditions.
(a) Hybrid delivery
Teaching Method 1 - Lecture
Description: Mix of on-campus/on-line synchronous/asynchronous sessions
Teaching Method 2 - Tutorial
Description: Mix of on-campus/on-line synchronous/asynchronous sessions

(b) Fully online delivery and assessment
Teaching Method 1 - Lecture
Description: On-line synchronous/asynchronous lectures
Teaching Method 2 - Tutorial
Description: On-line synchronous/asynchronous sessions

(c) Standard on-campus delivery
Teaching Method 1 - Lecture
Description: Mix of on-campus/on-line synchronous/asynchronous sessions
Teaching Method 2 - Tutorial
Description: On-campus synchronous sessions

### Teaching Schedule

 Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL Study Hours 36 10 46 Timetable (if known) Private Study 104 TOTAL HOURS 150

### Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
(533) Final Exam. There is a resit opportunity. This is an anonymous assessment.  2.5 hours    60
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
(533.1) Theory assignment 1. There is a resit opportunity [a part of the resit exam].  5 hours    10
(533.2) Theory assignment 2. There is a resit opportunity [a part of the resit exam].  10 hours    10
(553.3) Programming assignment There is a resit opportunity [a part of the resit exam]  10 hours    10
(533.4) (Video) presentation. There is a resit opportunity [a part of the resit exam].  10 hours    10

### Recommended Texts

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