The A+ Student's Guide to Math Online
We live in an era driven by technological capabilities, which includes understanding of many different subjects in Science, Technology, Engineering, and Math (STEM). However, from those four categories, all of them depend on a solid capability in mathematics.
Whether you're using trigonometry to develop a GPS app, testing the electrical current on a robotic servo-motor, or using a complex formula to control the camera in a game engine, all technical jobs require a strong understanding of many different forms of math.
Math Student Tips
Elementary & Middle School Math Skills
The starting point for all mathematics is the ability to understand numbers with counting, comparison, which eventually leads into multiplication, division, the decimal system, negative numbers. Most students will finish up elementary school mathematics with basic probabilities, fractions, ratios, square roots and graphs
Middle school is generally characterized by understanding of geometry using Pythagorean theorem, addition of angles, linear functions, and introduction to algebra.
Early Math Pro Tip: repetition is key in this stage. Gamification can help aide in memorization and will increase the amount of time spent becoming familiar with concepts.
High School Math Skills
Algebra is the cornerstone of almost all useful math, the use of symbolic logic is critical for nearly all more advanced concepts, it is also necessary for using variables in computer programming. High school students learn to use algebra for solving the quadratic equations, but then begin to learn graphing, higher level geometry, and a strong focus on trigonometry.
Advanced high school students will learn about complex numbers, probability distribution, vector math, series math, all leading towards calculus. Most advanced students will take a year or two of calculus prior to graduation. Understanding calculus is absolutely essentially for any science or engineering degree, and strongly recommended even for information technology students.
High School Math Pro Tip: Trig, Trig, Trig, knowing the trig identities will prove extremely useful in more advanced concepts. Look for practice problems that require a lot of charts & graphs. For really adventurous students, an early introduction to negative numbers in trig with Euler's formula can be helpful.
Advanced Math Skills
In college, or any other learning program after high school, the focus on math skills will be geared towards a greater understanding of calculus. This means understanding both derivatives and integration extremely well, being able to understand how an integration works, but also memorizing important shortcuts and tricks.
Parallel to an understanding in raw calculus, students are challenged to become more familiar with vectors and are introduced to the concept of matrix math. Dealing with matrices means relearning a whole new way to do addition, multiplication, and understanding operations as an abstract concept.
From here, calculus can be extended to work in three dimensions, and the use of multiple systems of differential equations are introduced. Students here will learn that some questions have more than one answer, and will start using matrix math to solve complex differential calculus problems.
Any study beyond that becomes more specialized or applied. Math majors in University learn a variety of methods, but most ultimately use a "proof" system to demonstrate mastery of the subject. Things such as set theory and tensor math will be useful for physical sciences, and concepts in statistics apply to almost all fields of study.
Advanced Learning Pro Tip: get familiar with computing software. Mathematica can help with calculus extremely well. Learning how to do numerical integration in a programming language can also be deeply enlightening for science students. Also, find or start study groups as often as possible.
Applied Math Skills
Outside of academia, math is still used in a variety of ways. Programming requires a strong understanding of logic, which can be a type of math.
- Set theory is useful for understanding arrays, and series functions with matrix math is useful for manipulating those arrays.
- Trigonometry is useful for almost anything related to Geographic Information Systems, which has to do with position data and defining shapes or angles for determining boundaries.
- Calculus is nearly universal for any form of engineering or statistics. Any company which says it is working with "big data" should be able to understand the rate of change in trends so as to make strong predictions.
Even non-technical jobs require a strong understanding of math. Anyone working in business will need to be able to estimate percentages, plot trend-lines to determine growth rates, and be able to balance an account with just simple algebra. This can be true whether a business is in retail, food services, or in internet applications.
Applied/Workforce Math Pro Tip: keep some of your more useful school books around, Wikipedia won't have practice problems to retrain you with.
Khan Academy This site provides interactive challenges and assignments that you can use to improve your math skills. Select your current math level, and go at your own pace as you learn, solve, and improve. When you get stuck, hints and videos are available to help you out.
MIT Open Courseware Many different courses on a variety of topics, many covering concepts in advanced math.
Math Courses at Coursera Offering classes which are live video lectures, online projects, and more, take classes for free or pay for a certificate. Set at many different levels of experience.
Math Inspiration Sites
21 Seriously Cool Careers That Need Math Read about some careers that require good math skills. Brief sections are included for professions, such as animator, architect, science journalist, interior designer, and more.
Five Historic Female Mathematicians You Should Know This article provides brief biographies of five prominent mathematical geniuses who just happened to be females. Profiles include those of Sofia Kovalevskaya, Emmy Noether, Ada Lovelace, and more.
National Center for Education Statistics Read interesting facts about education and mathematicians, play math games, take quizzes and improve your overall problem-solving skills.
Famous Math Majors This resource provides a list of famous people who were all math majors.
Making Math Fun Article to show your parents so they can discover various ways to make learning math more fun for you.
K-12 Teaching Tools
Talking Calculator Have fun solving math problems with this talking calculator that can solve everything from addition and subtraction to multiplication and division.
Academic Skill Builder Games This website produced at the University of Kansas makes learning fun. If features a variety of games that can improve and challenge your math skills without you even realizing it. The site also features sections for help with homework, trivia and cool videos.
E-Learning for Kids As a global nonprofit foundation, e-learning for kids provides free online courses in math, science, keyboarding, and reading for youngsters ages 5 to 12. Pick your grade level and start using this colorful, animated site to hone your math skills in a fun way.
National Library of Virtual Manipulatives This site provides links to hundreds of interactive, virtual tutorials, which can help you better understand and visualize concepts that you might come across during your everyday math study.
Funbrain Challenge your math skills using this online educational playground. Find games that require you to solve fractions, figure out percentages, subtract, multiply, and more. Enjoy the colorful animations that make this website a fun place to learn.
Multiplication Math Games This website motivates quick thinking to solve math problems that are incorporated into games. In order to win the racing, flying, running, or flash-card games, you must solve the problems in a timely manner.
MangaHigh Math Games This website offers a selection of high-quality math games that can help improve your math skills. Play against other kids and win games by solving math problems in a timely fashion.
Educational Math Activities Play various math games that include fractions, multiplication, division, addition and subtraction.
Open a Lemonade Stand Use mathematical skills to make business decisions while running a virtual lemonade stand.
Advanced Math Learning Tools
Calculus.org Sets of exams with answers, problems with step by step solutions, sample problems.
Calculus-help.com Flash videos and interactive exercises, focusing on video tutorials to demonstrate basic concepts in calculus.
MIT Open Courseware Multiple video lectures teaching several different concepts for calculus.
Princeton University Press Video lectures by Adrian Banner at Princeton, from the 2006 academic year, free of charge.
Math Career Information
Mathematical Association of America Learn about popular career choices you can make with a degree in mathematics.
Bureau of Labor Statistics Tease your brain by finding out how much money mathematicians can make. Find out what mathematicians do, and how to become one.
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