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Tom M. Apostol

Tom M. Apostol is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Tom M. Apostol rather than just read about it. In short: Tom Mike Apostol ( ə-POSS-əl; August 20, 1923 – May 8, 2016) was an American mathematician and professor at the California Institute of Technology specializing in analytic number theory, best known as the author of widely used mathematical textbooks, including Calculus in two volumes. Life and career Apostol was born on August 20, 1923, in Helper, Utah.

Tom M. Apostol — main illustration
Tom M. Apostol — illustration

Key takeaways

  • Tom M. Apostol belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Tom M. Apostol to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Tom M. Apostol from memory before moving on to harder problems.

Reference excerpt

Tom Mike Apostol ( ə-POSS-əl; August 20, 1923 – May 8, 2016) was an American mathematician and professor at the California Institute of Technology specializing in analytic number theory, best known as the author of widely used mathematical textbooks, including Calculus in two volumes.

Life and career Apostol was born on August 20, 1923, in Helper, Utah. His parents, Emmanouil Apostolopoulos and Efrosini Papathanasopoulos, were Greek immigrants. Apostolopoulos's name was shortened to Mike Apostol when he obtained his United States citizenship, and Tom Apostol inherited this Americanized surname. Apostol received his Bachelor of Science in chemical engineering in 1944, Master's degree in mathematics from the University of Washington in 1946, and a PhD in mathematics from the University of California, Berkeley in 1948. Thereafter Apostol was a faculty member at UC Berkeley, MIT, and Caltech. He was the author of several influential graduate and undergraduate level textbooks. Apostol was the creator and project director for Project MATHEMATICS! producing videos which explore basic topics in high school mathematics. He helped popularize the visual calculus devised by Mamikon Mnatsakanian with whom he also wrote a number of papers, many of which appeared in the American Mathematical Monthly. He also provided academic content for an acclaimed video lecture series on introductory physics, The Mechanical Universe. In 2001, Apostol was elected into the Academy of Athens as a Corresponding Member. He received the Lester R. Ford Award for expository excellence in 2005, 2008, and 2010. In 2012, he became a fellow of the American Mathematical Society.

Bibliography Apostol, Tom M. (1957). Mathematical Analysis: A modern approach to advanced calculus (1st ed.). Addison-Wesley. ISBN 0-201-00288-4. {{cite book}}: ISBN / Date incompatibility (help) Apostol, Tom M. (1961). Calculus, Volume 1: Introduction, with vectors and analytic geometry (1st ed.). Blaisdell. Apostol, Tom M. (1962). Calculus, Volume 2: Calculus of several variables with applications to probability and vector analysis (1st ed.). Blaisdell. Apostol, Tom M. (1967). Calculus, Volume 1: One-variable calculus, with an introduction to linear algebra (2nd ed.). Wiley. ISBN 0-536-00005-0. MR 0214705. Zbl 0148.28201. Apostol, Tom M. (1969). Calculus, Volume 2: Multi-variable calculus and linear algebra with applications to differential equations and probability (2nd ed.). Wiley. ISBN 0-471-00008-6. Apostol, Tom M. (1974). Mathematical Analysis (2nd ed.). Addison-Wesley. ISBN 978-0201002881. Apostol, Tom M. (1976). Introduction to Analytic Number Theory. Springer-Verlag. ISBN 0-387-90163-9. Apostol, Tom M. (1976). Modular Functions and Dirichlet Series in Number Theory (1st ed.). Springer-Verlag. Apostol, Tom M. (1990). Modular Functions and Dirichlet Series in Number Theory (2nd ed.). Springer-Verlag. ISBN 0-387-90185-X. Apostol, Tom M. (1997). Linear Algebra: A first course, with applications to differential equations. Wiley. ISBN 978-0471174219. Apostol, Tom M. (2008). The Mechanical Universe: Mechanics and heat, advanced edition (with Steven C. Frautschi, Richard P. Olenick, and David L. Goodstein ed.). Springer-Verlag. ISBN 0-521-30432-6. Apostol, Tom M. (2012). New Horizons in Geometry (with Mamikon Mnatsakanian ed.). MAA Press. ISBN 088385354X.

Notes

External links Tom M. Apostol, Professor of Mathematics, Emeritus, Caltech A VISUAL Approach to CALCULUS problems Tom M. Apostol at IMDb Project MATHEMATICS!

Illustrations

Tom M. Apostol illustration

Worked examples

Example 1 — a first encounter with Tom M. Apostol

Start with the simplest possible case. Write down what Tom M. Apostol claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Tom M. Apostol before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Tom M. Apostol ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Tom M. Apostol

In research
Tom M. Apostol appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Tom M. Apostol in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Tom M. Apostol is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1923 births, 2016 deaths, 20th-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Tom M. Apostol outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Tom M. Apostol in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Tom M. Apostol means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Tom M. Apostol out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Tom M. Apostol in simple terms?

Tom Mike Apostol ( ə-POSS-əl; August 20, 1923 – May 8, 2016) was an American mathematician and professor at the California Institute of Technology specializing in analytic number theory, best known as the author of widely used mathematical textbooks, including Calculus in two volumes. Life and care…

Why does Tom M. Apostol matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Tom M. Apostol?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Tom M. Apostol.

Tags

  • 1923 births
  • 2016 deaths
  • 20th-century American mathematicians
  • 20th-century Greek mathematicians
  • 21st-century American mathematicians
  • American number theorists
  • American people of Greek descent
  • American textbook writers
  • California Institute of Technology faculty
  • Corresponding Members of the Academy of Athens (modern)
  • Fellows of the American Mathematical Society
  • MIT School of Science faculty

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