MMW prelims

Mathematics

Study of relationships among numbers, quantities, and shapes.

Geometry

Branch of mathematics concerned with the shape of individual objects, spatial relationships among various objects, and the properties of surrounding space.

Patterns

A sequence or designs that are orderly and that repeat.

David Hilbert

Father of Patterns or Geometry; influenced modern mathematics within his axiomatic treatment of geometry.

Numeric Patterns

Consists of numbers where common connection lies among the numbers of the pattern.

Random Numerical Pattern

Example: 12 months of the Gregorian Calendar.

Systematic Numerical Pattern

Example: Divisible by 2.

Geometric Patterns

Consists of shapes and colors.

Symmetry

When different sides of something are alike; Reflection.

Spirals

A coiled or curved pattern that focuses on a center point and a series of circular shapes that revolve around it.

Fractals

Are the 'never-ending' patterns that repeat indefinitely as the pattern is iterated on an infinitely smaller scale.

Fibonacci Pattern

The sequence of numbers that goes 1, 1, 2, 3, 5, 8, 13, 21...and so on.

Tessellations

Are patterns that are formed by repeated cubes or tiles.

Technology

Mathematics is the language of science and technology.

Cryptography

Relies heavily on advanced mathematical concepts such as number theory, abstract algebra, and probability theory.

Computer Graphics

Mathematical transformations, such as matrices and vectors, are fundamental to computer graphics.

Machine Learning and Artificial Intelligence

Mathematics, particularly linear algebra, calculus, and probability theory, underpins machine learning and artificial intelligence algorithms.

Optimization

Optimization methods are used to solve complex problems with the aim of finding the best solution among various possibilities.

Robotics and Control Systems

Mathematics is essential for modeling and controlling robotic systems.

Network Theory

Mathematics is used in analyzing and optimizing network structures, such as computer networks, social networks, and transportation networks.

Engineering

In engineering, math is used to design and develop new components or products, maintain operating components, model real-life situations for testing and learning purposes, as well as build and maintain structures.

Examples of Use of Mathematics in Engineering

Examples include Construction, Automotive Design, Building Bridges, Robotics, Roller Coaster Design, Computer Circuits, Rockets and Satellites, and Microwaves.

Media

Mathematical concepts and themes can be found everywhere in the media, enhancing storytelling, simplifying complex concepts, and promoting critical thinking.

Critical Thinking

Media can influence the values, beliefs, and ideas of its audience, making it crucial for consumers to learn how to recognize sound and usable data amidst a vast amount of numbers and statistics.

Graphics and Visuals

Digital media offers new ways to represent and manipulate mathematical concepts, making it easier to visualize complex ideas and engage students in learning mathematics.

Accuracy and Realism

Mathematics ensures the accuracy and realism of different aspects of media, such as movies and television shows.

Science Fiction and Fantasy

Mathematics is used to create futuristic or fantastical worlds, including constructing intricate imaginary languages, creating visually stunning landscapes or buildings, and designing complex puzzles for characters to solve.

News Reporting

The media frequently uses numbers to report on topics such as unemployment rates, consumer price index (CPI), gross domestic product (GDP), high school dropout rates, and life expectancy.

Sports Statistics

Widely used in the media to provide insights into games and athletes' performances, including player statistics, team rankings, and game predictions.

Stock Market Data

Media outlets often report on stock market trends and financial news, which involves interpreting and presenting complex financial data.

Mathematics Education

Mathematicians and educators use media to communicate mathematical concepts and issues in education and research funding to the general public.

Medicine and Health

Math has been a crucial component of modern medicine, seen in diagnostic imaging interpretation, optimal drug regimen calculation, and epidemiologic modelling.

Examples of Use of Mathematics in Medicine and Health

Examples include Dosage Calculations, where healthcare professionals calculate medication dosages based on factors such as a patient's weight, age, and medical condition.

Dosage Calculations

Healthcare professionals frequently calculate medication dosages based on factors such as a patient's weight, age, and medical condition.

Intravenous (IV) Flow Rate

The rate (in milliliters per hour) at which fluids or medications are administered intravenously.

Body Mass Index (BMI)

A measure of body fat based on a person's height and weight, calculated by dividing weight in kilograms by the square of height in meters (BMI = weight / height^2).

Graphs and Statistics in Medicine

Tools used by medical professionals to show success rates of treatments and understand the effectiveness of different medical interventions.

Quantitative Sciences

Fields of study that integrate knowledge to understand the biology underlying different disease states and improve patient care.

Research Journal

Mathematics in Medical and Life Sciences, which focuses on mathematical sciences relevant to current questions in medicine, biology, and life sciences.

Patient Care

The application of mathematics to predict and measure the impact of diseases on populations and to treat patients.

Mathematics in Finance and Business

Essential tools for analysis, decision-making, and problem-solving in finance and business.

Business Ownership

Requires skills beyond product creation, including financial oversight for survival and success.

Basic Business Math

Necessary for profitable operations and accurate record keeping in business.

Examples of Use of Mathematics in Finance

Includes supply chains, finance and banking, gambling, insurance, loans, fraud detection, big data, pricing strategies, and game theory.

Language

A complex system of words and symbols used by a community for communication.

Nouns

Words referring to persons, places, things, and ideas, used to name things.

Pronouns

Words that replace nouns in a sentence.

Verbs

Words expressing actions, occurrences, or states.

Adjectives

Words that modify or describe nouns and pronouns.

Adverbs

Words that modify or describe verbs, adjectives, or other adverbs.

Prepositions

Words that show relationships between words or phrases.

Conjunctions

Words that connect words, phrases, or clauses.

Interjections

Words that express emotion or feeling.

English Sentence

Used to state a complete thought.

Mathematical Language

An arrangement of mathematical symbols used to represent a mathematical object of interest.

Numbers

Are the very first symbols that can be used to represent quantity.

Operation Symbols

Can act as connectives in mathematics.

Relation Symbol

Are used for comparison and act as verbs in the mathematical language.

Grouping Symbol

Are used to associate groups of numbers and operators.

Variables

Are letters that represent quantities and act as pronouns.

Mathematical Expression

An expression is the name given to a mathematical object of interest. Does not state complete thought.

Mathematical Sentence

It is a correct arrangement of mathematical symbols that states complete thought.

Precise

Refers to the quality, condition of being exact and accurate.

Concise

Able to say things briefly.

Powerful

Able to express complex thoughts with relative ease.

Set

A set is a collection of objects, and in mathematical discourse, these objects are mathematical ones such as numbers, points in space, or other sets.

Function

One of the most basic activities of mathematics is to take a mathematical object and transform it into another one.

Relation

The phrase 'less than' in a sentence.

Elementary Logic

Logic allows us to test whether propositions or arguments are valid or invalid.

Logical Connectives

Is a symbol or a word which is used to connect two or more sentences.

Negation

Is the opposite of a statement, usually employing the word 'not'.

Conjunction

Is a compound sentence formed by using the word 'and' to join two simple sentences.

Disjunction

Is a compound sentence formed by using the word 'or' to join two simple sentences.

Implication

A type of relationship between two statements or sentences.

3 Meanings of the word 'is'

5 is the square root of 25, 5 is less than 10, 5 is a prime number.