In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization―essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built.

This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization.

When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?”

This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, or machine learning.

About the Author:

Jeffrey Humpherys is a research professor at the University of Utah School of Medicine. He was formerly a professor of mathematics at Brigham Young University, where he received a National Science Foundation CAREER award. He has a longstanding commitment to applied mathematics education. In addition to serving two terms on the SIAM Education Committee, Professor Humpherys also helped form the SIAM Activity Group on Applied Mathematics Education, where he served as the inaugural vice chair. His research spans a wide range of topics in applied and computational mathematics, from nonlinear partial differential equations to machine learning in healthcare.

Tyler J. Jarvis is a professor of mathematics at Brigham Young University whose research has primarily been in geometric problems arising from physics. He is the recipient of a National Science Foundation CAREER award and the Mathematical Association of America's Deborah and Franklin Tepper Haimo Award for Distinguished University Teaching of Mathematics.

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