Math Topics
Algebra
Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions.
Analytic Geometry
In classical mathematics, analytic geometry is the study of geometry using a coordinate system.
Probability/Combinatorics
The science of counting is captured by a branch of mathematics called combinatorics. The concepts that surround attempts to measure the likelihood of events are embodied in a field called probability theory.
Calculus
Calculus studies the behaviour of functions of a single variable.
Trigonometry
The branch of mathematics concerned with specific functions of angles and their application to calculations
BIOGRAPHY
DR. ASTANEH
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For many students at any level, the Teachers/Instructors they learn from in schools, colleges and universities become influential figures in their future careers. The author of this website has had the pleasure of witnessing many of his past students having successful careers, whether teaching in universities, working in technology sectors or having high positions in other industries.
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As for a biography of Ali Astaneh, he did both his Masters and Ph.D. at the University of London, England, in 1977 in Mathematical Analysis. He began teaching at the University of Ferdowsi in Mashhad, Iran leading to the headship of the Department of Mathematics in early 1984 while holding an Associate Professorship position. In September 1985, he went to the University of British Columbia as a Visiting Professor. For the next 12 years, he mainly taught at UBC, but also taught for 3 to 4 years at Simon Fraser University, Langara College and Okanagan College in Kelowna, in various positions, mainly as an Instructor or Assistant Professor in short-term contracts. Finally, in September 1998, he joined the Vancouver School Board as a Senior Math Teacher until his retirement.
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The content of this website is mostly Ali's works/findings since he became a secondary school math teacher. However, many of his findings are at the university level. During this period, he has frequently posted his findings on the BC Association of Math Teachers' e-mail list, mainly in the form of Math-typed PDF attachments. At the recommendation of some colleagues in 2018, he was encouraged to create this website. As readers of this website will realize, most of the material is original works that are not recorded elsewhere. Examples include a new method of factoring and solving polynomials (refer to the Multipliers Algorithm in Algebra section), a variety of Analytical Geometric Characterizations for Parabolas (refer to Calculus 1 section), together with one such Characterization for Cubic curves. In particular, his method of Implicit Integration (refer to Calculus 2 section) presents a new method of integration for some implicitly defined functions, leading to the introduction of a new class of differential equations termed Abnormal Differential Equations and their solutions (refer to the Calculus 2 section). And finally, his recent January 2022 formulation of an exact count for the central integer (Mu) in Gauss's Lemma and the analytical geometric interpretation of the cardinality (refer to the Number Theory section).
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Having said all of that, this website's ultimate goal has been to include interesting materials for all levels of math, starting from elementary and going all the way up to the university level.
