Introduction to Mathematics

Math

• Math is the study of numbers, quantities, shapes, and their relationships using mathematical notations and operations.
• Arithmetic involves basic operations such as addition, subtraction, multiplication, and division.
• Algebra uses symbols and letters to represent numbers and quantities in formulas and equations.
• Geometry deals with shapes, sizes, positions, and properties of space.
• Calculus involves the study of continuous change, rates, and accumulation, and includes differential and integral calculus.
• Statistics is the science of collecting, analyzing, interpreting, and presenting data.
• Trigonometry studies the relationships between angles and sides of triangles and trigonometric functions.
• Number theory explores the properties and relationships of numbers, especially integers.
• Discrete mathematics deals with mathematical structures that are fundamentally discrete rather than continuous.
• Topology studies properties of spaces that are preserved under continuous deformations.

Chemistry

• Chemistry is the study of matter and its properties as well as how matter changes.
• Matter is anything that has mass and takes up space; it exists in states: solid, liquid, gas, and plasma.
• An element is a pure substance consisting only of atoms that all have the same numbers of protons in their nuclei.
• A compound is a substance consisting of two or more different elements chemically bonded together in a fixed ratio.
• Atoms are the basic units of matter, consisting of protons, neutrons, and electrons.
• Molecules are formed when two or more atoms are joined together by chemical bonds.
• Chemical reactions involve the rearrangement of atoms and molecules to form new substances.
• Stoichiometry is the calculation of relative quantities of reactants and products in chemical reactions.
• Acids are substances that donate protons or accept electrons, while bases accept protons or donate electrons.
• Organic chemistry is the study of carbon-containing compounds and their properties.
• Thermochemistry studies the heat and energy associated with chemical reactions and physical transformations.

Physics

• Physics is the study of the fundamental laws and principles governing the universe, including motion, energy, force, and matter.
• Mechanics deals with the motion of objects and the forces that cause them.
• Thermodynamics studies the relationships between heat, work, and energy.
• Electromagnetism deals with the interactions between electric currents or fields and magnetic fields.
• Optics studies the behavior and properties of light, including reflection, refraction, diffraction, and interference.
• Quantum mechanics studies behavior of matter and energy on the atomic and subatomic level.
• Nuclear physics studies the structure, properties, and reactions of atomic nuclei.
• Relativity includes special relativity (relationship between space and time) and general relativity (gravity as a curvature of spacetime).
• Acoustics studies the production, control, transmission, reception, and effects of sound.
• Astrophysics applies physics to astronomical objects and phenomena.
• Condensed matter physics studies the macroscopic and microscopic properties of matter, including solids and liquids.

Biology

• Biology is the scientific study of life and living organisms.
• Cells are the basic units of life and are responsible for carrying out all life processes.
• Genetics is the study of heredity and the variation of inherited characteristics.
• Evolution is the process by which populations of organisms change over time.
• Ecology is the study of the relationships between organisms and their environment.
• Anatomy is the study of the structure of organisms.
• Physiology is the study of the function of organisms.
• Microbiology is the study of microorganisms such as bacteria, viruses, and fungi.
• Botany is the scientific study of plants.
• Zoology is the scientific study of animals.
• Biochemistry studies the chemical processes within and relating to living organisms.

English

• English involves language, literature, composition, and comprehension.
• Grammar involves the rules governing the structure of sentences and the use of words.
• Vocabulary focuses on words and their meanings.
• Composition involves writing effectively and coherently.
• Literature includes the study of various forms of writing, like novels, poems, and plays.
• Reading comprehension means understanding the meaning of written texts.
• Rhetoric studies the art of effective or persuasive speaking or writing.
• Linguistics is the scientific study of language and its structure.
• Semantics studies the meaning of words, phrases, and sentences.
• Pragmatics studies how context contributes to meaning in language.
• Creative writing includes genres like fiction, poetry, and drama.