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

Challenges

We will be working on these challenges in the lab session for this topic.

You do not have to complete these in advance. However you may choose to get started on them in advance if you wish. You still need to attend the lab even if you have completed the challenges! If you do not complete them in the lab it is recommended that you finish them in your own time.

Set Theory Question Generator

Click “Generate” to generate a list of questions. Copy them to a separate file and then give answers for each of them. If you don’t know how to do a question, look it up in the lecture notes or ask me. Keep going until you feel confident in answering all of the questions that appear.

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Implementing Sets

Java only has a very limited set interface. It is not sufficient if we want to perform standard set theory operations such as intersection and union.

Task 1

Implement a Set class that provides the following interface:

int cardinality() - Returns the number of elements in the Set
boolean subset(Set b) - Returns true if this set is a subset of set b.
boolean superset(Set b) - Returns true if this set is a superset of set b.
Set union(Set b) - Returns a new set that is the union if this set and the provided set b
Set intersection(Set b) - Returns a new set that is the intersection of this set and the provided set b
Set difference(Set b) - Return a set representing the set-theoretic difference between this set and a provided set b.

Task 2

The power set of a set is the set of all its subsets. For example, the power set of the set {1, 2, 3} is { Ø, {1}, {2}, {3}, {1,2}, {2,3}, {1,2,3} }

Add a method Set powerSet() to your class which returns the power set of this set.

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Getting Started

Introducing Mathematics