Numerical Systems

Introduction Positional Notation Converting Between Bases Binary Addition Binary Multiplication Challenges (Python) Challenges (Java)

Modular Arithmatic

Introduction The Modulus Operator Cyphers Modular Arithmetic Modular Inverse Challenges (Java)

Algorithms

Introduction Algorithms Time Functions Asymptotic Complexity Summation Challenges

Propositional Logic

Introduction Propositional Logic Conjunction and Disjunction Implication and Equivalence Bitwise Operators Challenges

Set Theory

Introduction Sets Subsets and Supersets Set Operations Challenges

Graph Theory

Introduction Graphs Directed Graphs Structure of Language Search Trees Neural networks Game Object Trees Challenges Graph Question Generator

Proof

Introduction Proof Proof by Cases Proof by Contradiction Proof by Induction Challenges

Maths to Code

Maths to Code Challenges Question Generator

Descriptive Statistics

Introduction Statistics Measures of Central Tendency Measures of Spread Data Visualisation Correlation Challenges

Probability

Introduction Probability Basics Combinatorics Probability Trees Law of Total Probability Bayes Rule Challenges

Inferential Statistics

Introduction Probability Distributions Samples and Populations Hypothesis Testing Z Scores Student's T-Test Challenges

Statistics

In this section we’re going to gain an overview of statistics, what it is, and ways in which it is used.

Ten-minute video

You can also view this video on YouTube

You can find the slides here and also as .odp.

Key Points

Numeric/Scalar data is data which has ordering and the ratio between values is meaningful. For example a student who gets 10 marks not only got more marks than another who got 5, but we can say they got twice as many.

Ordinal data is data which has ordering, but the ratio between values is not meaningful, such as most answers on a scale from 1-5. Answering 2 means you agree more than 1, but not necessarily twice as much.

Nominal data is data with values like: “cat”, “dog”, “no pet”. It has no natural ordering.

Descriptive Statistics describes properties of our data. For example, the count of occurances of a particular value would be a descriptive statistic.

Inferrential Statistics are used to infer things about the world from our data

Hypothesis Testing is where we have an idea about the way the world might be, and perform a statistical analysis to test what the likelihood is that this hypothesis is false.

Questions

1. Check your understanding

For each of the types of data, say whether they are nominal, ordinal, or numeric

	Expression	Nomainal	Ordinal	Numeric
1.	Idle temperature of a CPU
2.	Gender
3.	Age
4.	Height
5.	Paper size (A3, Fullscap, Letter, A4, etc.)
6.	Dog breed ordered by average height

Check Answers —

Summary

In this section we have been introduced to statistics.

You should know the meanings of the terms introduced above.

In the next section we learn about measures of central tendancy.

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Getting Started

Introducing Mathematics