Jstewart
What does the major Mathematics - General cover ?
I am an 11th grader and I plan on majoring in Mathematics and I want to know the different fields of Mathematics so i can pick the right one for me or the one I think I would be the most interested in. #college-major #math
3 answers
Matt DeLand
Matt’s Answer
Hi jstweart,
Great question! Most high school students don't get a lot of exposure to the different areas of mathematics - partly because of curriculum design and partly because some areas require more advanced background knowledge. There are two major divisions within mathematics - pure (or theoretical) and applied. Applied mathematics can refer to statistics, or computational issues, and also focus on engineering issues. Pure mathematics has a few major subdivisions, analysis, algebra, geometry, and topology (other people might give you a slightly different list). You can read about these areas of study here, http://en.wikipedia.org/wiki/Areas_of_mathematics, but they're also very broad and there are many specializations available within each division. If you have specific questions, don't hesitate to ask!
Most math major programs require that you take at least a couple courses in different sub-divisions so that you have a feel for what's out there. There is also usually some course in each major that focuses on how to write proofs and think about things abstractly (sometimes this is real analysis, sometimes it's linear algebra, it just varies by school). It's important to take this course soon in your college career, to get a feel for abstract math and also to meet the other math majors and professors who you will be working with along the way. You don't have to have settled on a sub-discipline of math when you walk in to your first class - students are often swayed (rightly so!) by the courses offered and the professors teaching the course. My advice would be to expose yourself to many different kinds of math before you choose to specialize in any single one. Good luck!
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I am now a college student and I am still considering Mathematics as my major so this was very help, I just really have to look into it and do more research. Thank you
Jstewart
Daniel Jarratt
Daniel’s Answer
Often high schools and colleges offer statistics in a different major or course than general math. I highly suggest you look into statistics if you like math: stats is a fast-growing field with a lot of job options and relatively high pay. It's also a lot of fun!
The best way to figure out what part of math/stats you like best is to read about them online, try fun problems of your own, and see what sort of careers people have. For instance, many statisticians got their start because they love playing with sports data. Software engineers loved creating games. Theoretical mathematicians loved trying new proofs for famous problems. In short, see what's fun about the fields and give it a shot!
thank you, this was really helpful.
Jstewart
James Constantine Frangos
James Constantine’s Answer
What Does the Major Mathematics - General Cover?
Overview of Mathematics as a Major
Mathematics is a broad and diverse field that encompasses various areas of study. A major in Mathematics - General typically provides students with a comprehensive foundation in mathematical theories, principles, and applications. This major is designed to equip students with problem-solving skills, analytical thinking, and quantitative reasoning abilities that are essential for various careers.
Core Areas of Study
Pure Mathematics: This area focuses on abstract concepts and theoretical frameworks. Key subjects include:
Algebra: The study of mathematical symbols and rules for manipulating these symbols.
Calculus: The examination of change through derivatives and integrals.
Geometry: The exploration of shapes, sizes, relative positions, and properties of space.
Number Theory: The investigation of integers and their properties.
Applied Mathematics: This branch applies mathematical methods to solve real-world problems. Important topics include:
Statistics: The collection, analysis, interpretation, presentation, and organization of data.
Operations Research: The application of mathematical methods to decision-making processes.
Numerical Analysis: The study of algorithms for approximating solutions to mathematical problems.
Mathematical Logic and Foundations: This area deals with the formal logical structure underlying mathematics. It includes:
Set Theory: The study of sets or collections of objects.
Proof Techniques: Understanding how to construct valid arguments in mathematics.
Discrete Mathematics: This field involves the study of mathematical structures that are fundamentally discrete rather than continuous. Topics include:
Graph Theory: The study of graphs as a representation of pairwise relationships between objects.
Combinatorics: The branch concerned with counting, arrangement, and combination.
Advanced Topics (Electives): Depending on the institution, students may have the opportunity to explore specialized areas such as:
Topology: The study of properties preserved under continuous transformations.
Differential Equations: Equations involving derivatives that describe various phenomena in engineering and science.
Interdisciplinary Applications: Many mathematics programs encourage students to apply their knowledge in other fields such as physics, computer science, economics, or engineering through interdisciplinary courses or projects.
Research Opportunities and Capstone Projects: Some programs may offer research opportunities where students can engage in original research or complete capstone projects that synthesize their learning experiences.
Career Pathways Post-Graduation: Graduates with a degree in Mathematics can pursue various career paths including but not limited to:
Actuary
Data Analyst
Statistician
Operations Research Analyst
Educator
In summary, a major in Mathematics – General covers a wide array of topics that prepare students for both theoretical understanding and practical application across multiple disciplines.
Top 3 Authoritative Sources Used:
American Mathematical Society (AMS): A leading organization dedicated to advancing research in mathematics through publications and conferences; it provides resources about different branches within mathematics.
Mathematical Association of America (MAA): An organization focused on enhancing the understanding and appreciation of mathematics; it offers insights into undergraduate programs and career opportunities related to mathematics.
National Council of Teachers of Mathematics (NCTM): A professional association that supports math education; it provides resources for educators which also reflect on curriculum standards relevant to college-level mathematics education.
GOD BLESS,
JC.