How the Internet Will Help Students Taking Higher Math Courses Succeed


G. Stolyarov II

See Mr. Stolyarov's Index of Selected Writings, Originally Published on Associated Content / Yahoo! Voices.
A sample image Note from the Author: This article was originally written in 2008 and published on Associated Content (subsequently, Yahoo! Voices). The article's fundamental concept is sound, but its references to sites like Associated Content are now obsolete. To preserve a record of my past writings following the shutdown of Yahoo! Voices in 2014, I have given this article a permanent presence on this page. 

~ G. Stolyarov II, July 22, 2014

When learning anything mathematical, the best way to do so is to work through example after example, internalizing formulas and concepts as one solves problems that involve them. If a solution key to the problems is available, then students can check their work to see if they are using the correct procedures. Because of abundant online sample problems and solutions on mathematical topics ranging from basic arithmetic to calculus, students from elementary school to early college can now learn these topics using some of the best freely available resources. With enough persistence doing enough practice problems, anyone with even average intelligence can learn math through the first or second year of college.

But this is not yet the case for higher mathematics - subjects students take after their calculus courses, including differential equations, linear algebra, abstract algebra, real analysis, topology, and graduate school-level topics. Since there are fewer students taking these classes - and fewer still qualified to write sample problems and instructional materials regarding them - the Internet still has not accommodated those students' need for problems to practice with as they learn. A similar scarcity of freely available practice problems exists in higher levels of fields that use mathematics - such as finance, economics, chemistry, physics, and biology.

But this has already begun to change. My Free Tools for Rational Education is the beginning of an effort to write and compile practice problems and solutions for higher mathematical fields. These resources have already been used by students preparing for tests, including the notoriously difficult actuarial Exam 3F/MFE. By writing and providing 423 free practice problems with solutions for actuarial students, I attracted tens of thousands of page views and enabled hundreds of actuarial students to get practice with challenging exam concepts.

Higher mathematics and exam preparation materials will always be in demand, as hundreds of thousands of students will continue to take courses and exams requiring such preparation. Rendering these materials free online will be a bargain for many students, who at present can only get enough higher mathematics practice by purchasing hyper-expensive textbooks and study manuals. If enough talented students write and publish problems and share their knowledge with others, a critical mass of materials will emerge, and increasing numbers of students will flock to the Internet as a versatile, abundant, and free resource of opportunities to practice with difficult concepts. Moreover, students seeking help on particular kinds of homework problems or concepts will know exactly what keywords to search for and are likely to quickly find pages containing those keywords. I expect that this will greatly enhance the accessibility of higher mathematics and contribute to a more knowledgeable population with greater opportunities before them.

Talented students will want to write practice problems because, with sites like Associated Content, they can earn a small but steady passive income by doing so. Free higher mathematics practice problems will continue to attract one class of students after another - and perhaps even future generations of students many decades from now.

Gennady Stolyarov II (G. Stolyarov II) is an actuary, science-fiction novelist, independent philosophical essayist, poet, amateur mathematician, composer, and Editor-in-Chief of The Rational Argumentator, a magazine championing the principles of reason, rights, and progress. 

In December 2013, Mr. Stolyarov published Death is Wrong, an ambitious children’s book on life extension illustrated by his wife Wendy. Death is Wrong can be found on Amazon in paperback and Kindle formats.

Mr. Stolyarov has contributed articles to the Institute for Ethics and Emerging Technologies (IEET), The Wave Chronicle, Le Quebecois Libre, Brighter Brains Institute, Immortal Life, Enter Stage RightRebirth of Reason, The Liberal Institute, and the Ludwig von Mises Institute.

In an effort to assist the spread of rational ideas, Mr. Stolyarov published his articles on Associated Content (subsequently the Yahoo! Contributor Network and Yahoo! Voices) from 2007 until Yahoo! closed this venue in 2014. Mr. Stolyarov held the highest Clout Level (10) possible on the Yahoo! Contributor Network and was one of its Page View Millionaires, with over 3,175,000 views. Mr. Stolyarov’s selected writings from that era have been preserved on this page.

Mr. Stolyarov holds the professional insurance designations of Associate of the Society of Actuaries (ASA), Associate of the Casualty Actuarial Society (ACAS), Member of the American Academy of Actuaries (MAAA), Chartered Property Casualty Underwriter (CPCU), Associate in Reinsurance (ARe), Associate in Regulation and Compliance (ARC), Associate in Personal Insurance (API), Associate in Insurance Services (AIS), Accredited Insurance Examiner (AIE), and Associate in Insurance Accounting and Finance (AIAF).

Mr. Stolyarov has written a science fiction novel, Eden against the Colossus, a philosophical treatise, A Rational Cosmology,  a play, Implied Consent, and a free self-help treatise, The Best Self-Help is Free. You can watch his YouTube Videos.Mr. Stolyarov can be contacted at

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Learn about Mr. Stolyarov's novel, Eden against the Colossus, here.

Read Mr. Stolyarov's new comprehensive treatise, A Rational Cosmology, explicating such terms as the universe, matter, space, time, sound, light, life, consciousness, and volition, here.

Read Mr. Stolyarov's new four-act play, Implied Consent, a futuristic intellectual drama on the sanctity of human life, here.