Introduction to Math and Physics

Study Notes

Mathematics is a systematic study of abstract concepts, including logic, quantities, and structures. It involves the use of symbols, equations, and proofs to explore relationships and solve problems.
Key branches of mathematics include algebra, geometry, calculus, number theory, and statistics.
Algebra deals with symbols and their relationships, including solving equations.
Geometry explores shapes, sizes, and spatial relationships.
Calculus involves the study of continuous change and rates of change.
Number theory examines properties of numbers.
Statistics focuses on data collection, analysis, and interpretation.
Mathematical concepts are used in various fields, including science, engineering, computer science, and economics.
Mathematical tools are essential for modeling and understanding phenomena in the natural and human worlds.

Physics is the natural science that involves the study of matter, its motion and behavior through space and time, and related concepts such as energy and force.
It's concerned with understanding the fundamental laws of nature and how these laws govern the universe.
Key branches include mechanics, thermodynamics, electromagnetism, optics, and quantum mechanics, amongst others.
Mechanics focuses on motion and forces acting on objects.
Thermodynamics deals with heat, temperature, and energy transfer.
Electromagnetism studies electric and magnetic fields, their interactions, and related phenomena.
Optics investigates the behavior of light, including reflection, refraction, and interference.
Quantum mechanics explores the behavior of matter and energy at the atomic and subatomic level.
Physics utilizes mathematical tools to describe and predict physical phenomena.
Applications of physics are widespread, such as in the development of new technologies, the understanding of astronomical phenomena, and the design of medical equipment.