A Guide to Statistics First Year for Incoming Students: Core Modules
In this blog I’ll talk about the academic side of first year with some tips on what to expect, what to consider for the future, and where to get help and advice. First, let’s go through the core modules. At Warwick, each module is worth a certain number of CATS (what we call academic credits). In first year they are either 12 or 24, with the minimum per year needed being 120. Note that in first year the only difference between Morse and MathStat is that the economics module worth 24 CATS is not core and the operations research module worth 12 CATS is not core. Data Science is a whole nother ball game, so I’ll talk about core modules for Morse and DS in a later blog
Core for All Three Degrees:
ST116 – Mathematical Techniques:

Worth 12 CATS, taught in term 1

Introduction to mathematical language, ways of thinking, and proofs. A nice gentle start to your mathematical career, and always taught by the kindest and sweetest professor they can find.

Not compulsory to pass this module to pass the year, but it’s very easy to score highly to pull up your average. I like this module, it’s important to nail how something is done, just as much as it is important to know what to do. You understand how and you can apply it to many other unknown problems.
MA138 – Sets and Numbers:

Worth 12 CATS, taught in term 1

Introduction to mathematical foundations such as functions, basic linear algebra, and groups. Focuses more on the abstract concepts than ST116, but in many ways is a sister module in so far as they both guide you towards the same goal of being more confident in how to do university level mathematics.

Also not compulsory to pass, but is slightly more difficult than ST116 due to the higher level of abstraction and difficult concepts to grasp for the first time.
MA137 – Mathematical Analysis:

Worth 24 CATS, taught in terms 1 and 2

Where the real meat and potatoes of first year lies. This module is, roughly speaking, all about things getting smaller and smaller, and hopefully small “enough”. In term 2 you learn about sequences and series (sums of numbers), how they both can converge, and techniques to use to see if they do converge or not. Term 2 is all about how smooth functions are or, more formally, if they are continuous and differentiable. Think of y = x^2, this intuitively has both of these properties, but what about y= x? Sure, you can draw it without lifting your pencil off the paper, but what happens at y=0? There’s not a smooth curve, it’s a jagged 90 degree angle. Can you differentiate this? Finally, you’ll learn about functions that are neither of these things.

Can you tell that I loved this module? It’s definitely one of those “it’s impossible and confusing until it suddenly clicks” modules. To help this, try to explain things you just learned to a flatmate who knows nothing about maths past GCSE/Alevel. This is essentially what’s expected of you in exams so it’s good practice.

All modules from here on are compulsory to pass, this one included.
MA106 – Linear Algebra:

12 CATS, term 2

Introduces key concepts in the other key field of mathematics that are very useful to statisticians. Pay good attention to this module, especially if you want to do data science in the future as machine learning is essentially just applied linear algebra.

Another one of those “impossible till it clicks” module, but to a lesser extent than analysis as most people have done work with vectors and matrices before. The key difference now is that they are used more abstractly, and it’s this abstraction that needs to click.

From the start it’s useful to let go of the idea that vectors are directions in space. You will deal with vectors of 4 or higher dimensions (some even infinite) so this won’t help you and might even hinder your understanding if you think of everything as a direction in space.

Not too hard to score well in if you learn definitions and proofs, but this is generally true for maths modules.
ST115 – Introduction to Probability:

12 CATS, term 2

A difficult module if, like me, you had never done statistics or probability before. There is lots of content and lots to remember by heart.

Do yourself a favour and watch a youtube series on basic probability (careful that it doesn’t say “probability theory” that’s a different topic) before you tackle this module if you feel inexperienced in probability.

I can’t even list everything it teaches you about because it’s so much. But I can say that it is completely different from the Economics department’s statistics modules for first years in that it’s very theoretical and has nothing to do with tests and chisquare and the like. In fact, Econ students actually end up knowing more applied statistics than Stats students do, and they learn about things that Stats students only cover in 2nd year (in much more detail, but then this is also eclipsed by Econ students taking econometrics).
ST104 – Statistical Laboratory

12 CATS, term 3 (this runs during the time you generally revise for other exams)

“Introduction to Data Science with R” would probably be a more informative name, but “StatLab” rolls off the tongue easier.

In this module you learn about random sampling from distributions, summary statistics like the mean, median, and mode we all love, and some basic modelling with the programming language R

The assignments are about R, the exam is about the theory. This is important if programming is the last thing you want to be doing with your time frustrating as you can just get some conceptual help with the assignments and then score really well on the open book exam (notes allowed).