There are two sections that follow. The first is of top resources to actually learn mathematics online, including both Ivy League and for-credit resources. The second section is the best places to get answers to your questions and specific problems.


1. TITLE: Netmath Online
CONTENT: If college level credit bearing math courses is your game, then Netmath Online is the name. A top ranked science school, the University of Illinois @ Urbana Champaign has been offering distance learning to all types of learners through their Netmath program since 1991! Add to that the courses all utilize Mathematica software and are flexible in completion times and you have a real winner in the online education domain. NetMath offers 11 courses, ranging in 1 to 5 (most are 3) fully transferable college credits. The courses begin with College Algebra and go through Differential Equations and Advanced Calculus. This is a great way to learn college level math in an autodidactic fashion through some very powerful software.
USES: For the gifted high school student who wants college credit for mathematics courses this is a great option. For adult learners or college students who need math credit, this is great as well because the completion times are flexible and the credit transfers to almost every institution of higher learning. It is also a great site for learning Mathematica, an extremely powerful math software program.



2.TITLE: MIT Opencourseware
CONTENT: Whoa, whoa, this concept is really impressive. An ambitious goal of MIT is to have all their courses eventually ported online, and Open Courseware represents that dream manifested into a near reality. It ostensibly provides every element of the actual courses that are offered to a vast majority of current MIT students, the only thing missing is the actual professor interface. Although that is not entirely true either, some courses offer full length videos of actual classroom instruction! In which case you can pretend that the only difference between you and a real MIT student is you just can’t raise your hand for clarification! The site is designed well; no surprise considering this is MIT. Totally free, totally thorough and totally awesome!! (I mean like homepage one~!!!)
USES: For anyone that dreamt of a having an Ivy League education (for free?), Open Courseware is the closest thing to manifestation. While you cannot receive actual credit or a diploma, you can create for yourself or learners you are instructing a very close model of what an MIT education entails. For teachers the world over, it provides an amazing template for plugging and playing the MIT course structure for many classes. It also works great as an accompaniment to a class. For example when I was taking differential equations at my college locally I would watch the video lectures by the Professor Mattuck (a dedicated mit prof) on my laptop to supplement what I was learning in my actual class and it truly helped me digest the material better. And with the video lectures, I could even pause the professor to get a snack or go do something, try doing that in real life!




3. TITLE: Dr Physics
CONTENT: If I said for a nominal fee you could have a PhD in Physics from University of Chicago that would personally tutor you in the introductory Calculus and even some topics in Einstein’s theory of relativity, would that interest you? Well if it does than you should definitely check out Dr. Physics’ site. While these classes are not for college credit, the courses are rigorous and the knowledge you gain is invaluable. A pioneer in online education, Dr. Lombardi has testified to Congress about online education.
USES: For anyone that is interested in having direct access with a PhD in Physics to learn about Einstein’s theory of relativity this is a great option. It is also good for those learners that need to brush up or just want to learn about differential and integral calculus but don’t necessarily need or want college credit. I say that because the personal attention you receive from Dr. Lombardi is unparalleled. I say this from experience, now does anyone care to talk about time dilation?!

4. TITLE: Art of Problem Solving
CONTENT: This site can be thought of as math portal for eager math students in grades 7-12. It offers a forum for sharing insights and a variety of online classes. What really makes this site special are the people running it. It is a small but veritable brain trust of some of the most brilliant math minds; most are Ivy League educated and most have extensive and successful mathematical experience in math Olympiads and competitions. The site also offers plenty of information on books, articles, websites and other resources that pertain to mathematics and in particularly the art of problem solving. A site really borne out of the love of solving math problems, awesomeness!
USES: This is a great site for students who are very interested and/or talented in mathematics and want an opportunity to learn mathematics in a very personalized setting from some of the most talented mathematicians around today.



5. TITLE: Education Program for Gifted Youth
CONTENT: This is an ongoing research project through Stanford University. Its aim is to provide computer based multimedia courses in a variety of subjects that includes mathematics, physics, English, computer science and music. The main purpose of this project is to provide an outlet for gifted and talented youth everywhere. It gives these talented youngsters an opportunity to stay challenged and gain college credit in many cases. By not requiring geographic proximity to Stanford as well as lending their name, the EPGY program is an important example of how to cater to a population that is often not given an opportunity to maximize their potential.
USES: For any parent or educator that is under the care of a gifted child and is looking for ways to stimulate their child, this is a terrific educational option.


1. TITLE: Wolfram Mathworld

CONTENT: To call yourself “the web’s most extensive math resource” is almost asking for someone to prove you otherwise. After all, a recent Google search for the word mathematics yields a staggering 83.9 million results. Yet if you begin to spend some time on this site, it begins to dawn on you how true their claim really is. Between the subject and alphabetical organization of over 13,000 mathematical topics, you find the detail of explanations to be rigorous and thorough. They even offer detailed explanations of mathematics used in humor and pop culture! Many of the mathematical topics provide free downloadable Mathematica notebooks for further investigation and all topics have citations that are hyperlink annotated to books and resources. Considering this astonishing resource comes from the same guy that created Mathematica, Stephen Wolfram, it is not really a surprise. A PhD in Physics from Caltech by age 20, he makes most science geniuses look rather ordinary and apparently most math websites as well.
USES: This site is a great resource if you have or utilize the Mathematica software in your learning since it offers many free interactive Mathematica notebooks that can be downloaded to provide deeper insight on a topic. It carries a very reliable and authoritative voice as well so it is good for confirming or clarifying math questions.



2. Wikipedia Portal: Mathematics
CONTENT: While there always seems to be a swirl of controversy surrounding the accuracy of Wikipedia, it is truly astonishing the depth and quality of most of what you find on this site. With over 16,000 detailed articles pertaining to mathematics, the Wikipedia Portal for Mathematics would have seemed like some sort of utopian dream for mathematicians even a few short years ago! Virtually any concept or theory under the mathematical domain (and I am not speaking of the x axis lol) is covered, often with incredible precision and explanation. Furthermore, with so many terms being hyperlinked in any given article, cross referencing from one idea to the next is made easy. Perhaps the single most impressive site of all that I visited.

USES: If you ever have a term or concept in mathematics that you are unclear on, this resource will probably provide an answer for you. Furthermore if you are trying to look for further topics on an idea, the annotations at the end of each article usually provides places to find more insight on that idea. It is also great for boring down into a concept. For example if you are trying to learn more about differential equations, the article will not only provide a quality overview on differential equations but also link to specific types of differential equations, the history of differential equations, web resources on differential equations, graphs of differential equations etc.



3. TITLE: Ask Dr. Math
CONTENT: Ask Dr. Math is a question and answer service for math students and teachers. An impressive range of questions are meticulously answered at this site. The archive is fully searchable and you can also browse by level or math topic. The site has a bare bones layout but the detail and content more than makes up for it. This site is very good for clear explanations on many of the typical questions that arise in the studying of mathematics, from early topics in grade school to advanced topics in college science. A really great site for getting answers to specific math questions.
USES: The title gives away the best use of this site, namely to answer specific math questions. So for example, if you need to know what a vector is, why multiplying two negatives together makes a positive, what calculus is used for or even proving in a funny (not real!) way that 1 + 1 = 3, you will find detailed answers here. Often times typing your random math question in Google will yield a result that sends you to Ask Dr. Math. You have math questions, they have answers!



4. TITLE: A Maths Dictionary for Kids
CONTENT: On a decidedly different note, as the title suggests, this website is a math dictionary aimed at younger learners of mathematics. It contains over 500 common terms in mathematics explained in clear concise language. What is really unique about this site is the interactive nature of it. Most of the terms provided are explained with colorful pictures and require the user to engage in the definition. This interaction makes the learning of topics that are often presented in dry and abstract terms very real and clear.
USES: This is a great site for building lessons around important and fundamental math topics. It can be used as a resource for further elucidation on mathematical concepts that are not being fully absorbed by a learner. Each definition is presented in such a visual way that it is difficult not to understand what the idea is after reviewing it at this resource. Overall it makes for a great companion site alongside other learning tools to introductory ideas in mathematics.



5. TITLE: Springer Online Reference
CONTENT: It should be a well known fact to everybody learning mathematics that it is really a language onto itself. And since mathematics is to be considered a language every student engaged in the study of it must have ready access to some form of a math dictionary or encyclopedia resource. The Online Encyclopaedia of Mathematics is a very up-to-date and comprehensive graduate-level reference resource in the field of mathematics. This online math dictionary comprises more than 8,000 entries and illuminates nearly 50,000 notions in mathematics. It is a great site for students at the graduate or undergraduate level as it covers many advanced topics very well,
USES: For the student who has a specific math term that they need a detailed and comprehensive explanation of, this is a great site to visit.



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