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Students completing a year of Calculus can find novel and practical challenges in mathematics using numerical analysis. This text follows the mathematician's process of examining a problem and deciding which algebraic or calculus techniques lead to reliable solutions. Each algorithm includes all developmental steps, illustrating the beauty of reducing complex systems to streamlined formulae. Accessible proofs using techniques beyond those in geometry are fully explained. All algorithms contain detailed examples of success and situational pitfalls. An exhaustive set of practice problems was meticulously developed by hand, not AI-generated, ensuring deviations at each stage of a particular algorithm. Many exercises highlight advantages and disadvantages of algorithms through comparison.
Leon Galitsky has taught advanced level mathematics courses including multivariable calculus, linear algebra, and numerical analysis, for the past 26 years at Moravian Academy (secondary education). He received a B.S. from DeSales University, summa cum laude, with a dual major in mathematics and computer science and an M.S. from Lehigh University in applied mathematics in the department of mechanical engineering. Publications include a contributing author of a chapter in Survey of Text Mining: Clustering, Classification, and Retrieval and an editor of "A Survey of Emerging Trend Detection in Textual Data Mining". Both were early research forays into what is now considered AI. Other text mining research was conducted as an intern at the IBM research facility in Almaden, CA.