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MA12005: Statistics and data science 1A

[Page last updated: 03 June 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 15 [equivalent to 30 CATS credits]
Notional Study Hours: 300
Level: Certificate (FHEQ level 4)
Period:
Semester 1
Assessment Summary: CWRG 20%, EXCB 80%
Assessment Detail:
  • Probability & Statistics 1a (EXCB 40%)
  • Foundations (CWRG 20%)
  • Programming (EXCB 40%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Learning Outcomes: By the end of the unit, you will be able to:
  • Write pseudo-code and implement algorithms in Python; apply modern procedural programming paradigms in data science applications.
  • Apply the axioms and laws of probability to solve a variety of problems, including the use of combinations, permutations, and standard probability distributions.
  • Read and manipulate logical statements about mathematical objects, determine the validity of mathematical arguments, and formulate and write mathematical proofs using construction, contradiction, and induction.



Synopsis: You will develop core skills in statistics and computer programming with an emphasis on data science. You will develop a solid foundation in probability theory that will facilitate further study in probability and statistics. You will learn Python programming and sustainable software engineering for mathematics, include the design and analysis of algorithms and with examples from data science. You will also develop the ability to reason logically and to read and write mathematics well.

Content: Probability & Statistics: Sample space, events as sets, unions, and intersections. Axioms and laws of probability. Equally likely events. Sampling methods: with or without ordering and replacement. Conditional probability. Partition theorem. Bayes' theorem. Independence of events. Bernoulli trials. Discrete random variables (RVs). Probability mass function (PMF). Bernoulli, Geometric, Binomial and Poisson distributions. Joint and marginal discrete distributions. Definition of continuous random variables (RVs), cumulative distribution functions (CDFs) and probability density functions (PDFs). Some common continuous distributions including uniform, exponential and normal. Independence of RVs (including joint distribution as a product of marginals). Expectation of RVs. Properties of expectation. Expectation of product of independent RVs. Variance and properties. Standard deviation. Moments, covariance, correlation. Sums of independent random variables. Key application: Random walks. Statement of the law of large numbers. Programming & Data Science: Introduction to programming and programming paradigms. From specification through algorithms to implementation. Building elements: preconditions and postconditions; basic data types; variables, identifiers and scope; arrays and strings. Control structures: conditionals; loops. Correctness issues when programming with loops. Functions and subroutines: iteration and recursion.� Introduction to the design and analysis of algorithms: divide-and-conquer paradigm; sorting algorithms. Computational complexity of algorithms. Foundations: Study skills for mathematicians, including how to think and write logically, how to work with definitions, theorems and proofs, and techniques of proof, including construction, contradiction, and induction.

Course availability:

MA12005 is Compulsory on the following courses:

Department of Mathematical Sciences
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 1)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 1)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 1)

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.