# Tom M. Apostol

#2,574

Most Influential Person Now

American mathematician

## Tom M. Apostol's AcademicInfluence.com Rankings

Tom M. Apostolmathematics Degrees

Mathematics

#116

World Rank

#296

Historical Rank

#45

USA Rank

Measure Theory

#164

World Rank

#250

Historical Rank

#73

USA Rank

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Mathematics

## Tom M. Apostol's Degrees

- PhD Mathematics University of California, Berkeley
- Bachelors Chemical Engineering University of Washington

## Why Is Tom M. Apostol Influential?

(Suggest an Edit or Addition)According to Wikipedia, Tom Mike Apostol was an American analytic number theorist and professor at the California Institute of Technology, best known as the author of widely used mathematical textbooks. Life and career Apostol was born 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.

## Tom M. Apostol's Published Works

### Published Works

- Introduction to analytic number theory (1976) (3693)
- Mathematical Analysis (1957) (2019)
- Modular Functions and Dirichlet Series in Number Theory (1976) (1198)
- On the Lerch zeta function. (1951) (448)
- One-variable calculus, with an introduction to linear algebra (1967) (213)
- Generalized Dedekind sums and transformation formulae of certain Lambert series (1950) (168)
- An Elementary View of Euler's Summation Formula (1999) (147)
- Multi-variable calculus and linear algebra, with applications to differential equations and probability (1969) (129)
- Mathematical analysis : a modern approach to advanced calculus / Tom M. Apostol (1957) (111)
- Book Reviews: Mathematical Analysis. A Modern Approach to Advanced Calculus (1958) (82)
- Arithmetical properties of generalized Ramanujan sums (1972) (78)
- Another elementary proof of Euler''s formula for (2 ) n z (1973) (76)
- Dirichlet series related to the Riemann zeta function (1984) (62)
- Resultants of cyclotomic polynomials (1970) (55)
- The evaluation of Ramanujan’s sum and generalizations (1953) (54)
- Theorems on generalized Dedekind sums (1952) (53)
- A proof that euler missed: evaluating ζ(2) the easy way (1983) (53)
- Formulas for higher derivatives of the Riemann zeta function (1985) (50)
- Calculus, Volume 1 (1961) (48)
- Zeta and related functions (2010) (41)
- Calculus, Volume 1: One-Variable Calculus with an Introduction to Linear Algebra (1961) (38)
- Irrationality of The Square Root of Two—A Geometric Proof (2000) (37)
- A Primer on Bernoulli Numbers and Polynomials (2008) (35)
- Calculus, Volume II. (1962) (33)
- Explicit Formulas for Solutions of the Second-Order Matrix Differential Equation Y″ = ay (1975) (29)
- Dirichlet L-functions and character power sums (1970) (27)
- A New Method for Investigating Euler Sums (2000) (27)
- Some Explicit Formulas for the Exponential Matrix etA (1969) (25)
- Identities for sums of Dedekind type (1982) (25)
- Sums of Squares of Distances in m-Space (2003) (24)
- Elementary proofs of Berndt’s reciprocity laws (1982) (23)
- Unwrapping Curves from Cylinders and Cones (2007) (22)
- New Horizons in Geometry (2013) (21)
- Beyond the Mechanical Universe: From Electricity to Modern Physics (1986) (21)
- The resultant of the cyclotomic polynomials _{}() and _{}() (1975) (19)
- Some Properties of Completely Multiplicative Arithmetical Functions (1971) (19)
- The Tunnel of Samos (2004) (18)
- Addendum to ‘On the Lerch zeta function’ (1952) (17)
- The Mechanical Universe: Introduction to Mechanics and Heat (1985) (17)
- The approximate functional equation of Hecke’s Dirichlet series (1957) (16)
- A Fresh Look at the Method of Archimedes (2004) (14)
- Möbius functions of order k (1970) (14)
- Calculating Higher Derivatives of Inverses (2000) (14)
- Ptolemy's Inequality and the Chordal Metric (1967) (14)
- Solids Circumscribing Spheres (2006) (14)
- Some series involving the Riemann zeta function (1954) (14)
- A Visual Approach to Calculus Problems (2000) (13)
- A Course in Mathematical Analysis, Vol. II. (1965) (12)
- Elementary proof of the transformation formula for Lambert series involving generalized Dedekind sums (1982) (11)
- Tanvolutes: Generalized Involutes (2010) (11)
- The Mechanical Universe: Introduction to Mechanics and Heat and Beyond the Mechanical Universe: From Electricity to Modern Physics and The Mechanical Universe: Mechanics and Heat (Advanced Edition) (1986) (10)
- Subtangents—An Aid to Visual Calculus (2002) (10)
- Figures Circumscribing Circles (2004) (10)
- Euler’s -function and separable Gauss sums (1970) (10)
- Tangents and Subtangents Used to Calculate Areas (2002) (9)
- The method of sweeping tangents (2008) (9)
- A New Look at the So-Called Trammel of Archimedes (2009) (9)
- On the functional equation $F(mn)F((m,\,n))=F(m)F(n)f((m,\,n))$. (1964) (9)
- Calculus vol. 1 : one-variable calculus with an introduction to linear algebra / Tom M. Apostol (1967) (8)
- Calculus, volume II : multi - variable and linear algebra, with application to differential equations and probability / Tom M. Apostol (1969) (8)
- Finding Centroids the Easy Way (8)
- Calculus of several variables with applications to probability and vector analysis (1962) (8)
- Linear Algebra: A First Course with Applications to Differential Equations (1997) (8)
- The Story of PI (1989) (7)
- Remark on the Hurwitz zeta function (1951) (7)
- Dirichlet $L$-functions and primitive characters (1972) (7)
- Identities involving the coefficients of certain Dirichlet series (1951) (7)
- Selected papers on calculus (1971) (6)
- A Centennial History of the Prime Number Theorem (2000) (5)
- The Dedekind eta function (1976) (5)
- Sums of Squares of Distances (2001) (5)
- Isoperimetric and Isoparametric Problems (2004) (5)
- New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors (2008) (5)
- An extension of the Lehmers’ picturesque exponential sums (1993) (5)
- Binary vectors with prescribed subsets of consecutive ones (1988) (4)
- A short proof of Shô Iseki’s functional equation (1964) (4)
- Analytic Proof of the Prime Number Theorem (1976) (4)
- Centroids Constructed Graphically (2004) (4)
- Teaching Mathematics with Computer Animated Videotapes. (1991) (4)
- The Fundamental Theorem of Arithmetic (1976) (4)
- A Century Of Calculus (1992) (3)
- Surprising Geometric Properties of Exponential Functions (1998) (3)
- What Is the Most Surprising Result in Mathematics? Part II (1997) (3)
- Volume/Surface Area Relations for n-Dimensional Spheres, Pseudospheres, and Catenoids (2015) (3)
- ENERGY: CONSERVATION AND CONVERSION (1986) (3)
- 90.36 Bernoulli’s power-sum formulas revisited (2006) (3)
- Computer Animated Mathematics Videotapes (2002) (3)
- New Insight into Cycloidal Areas (2009) (3)
- Term-Wise Differentiation of Power Series (1952) (3)
- Area & Arc Length of Trochogonal Arches (2003) (2)
- New Balancing Principles Applied to Circumsolids of Revolution, and to n-Dimensional Spheres, Cylindroids, and Cylindrical Wedges (2013) (2)
- Introduction, with vectors and analytic geometry (1961) (2)
- Another Elementary Proof of Euler ' s Formula for ζ ( 2 n ) Author ( s ) : (2010) (2)
- Rademacher’s series for the partition function (1976) (2)
- Cycloidal Areas without Calculus (1999) (2)
- The Mechanical Universe: Preface (1986) (2)
- On magic squares constructed by the uniform step method (1951) (2)
- What Is the Most Surprising Result in Mathematics (1996) (2)
- Some Elementary Theorems on the Distribution of Prime Numbers (1976) (1)
- General Dirichlet series and Bohr’s equivalence theorem (1976) (1)
- Averages of Arithmetical Functions (1976) (1)
- A Note on Periodic Completely Multiplicative Arithmetical Functions (1976) (1)
- Proof Without Words: Surprising Property of Hyperbolas (2006) (1)
- Kronecker’s theorem with applications (1976) (1)
- The modular group and modular functions (1976) (1)
- 87.02 Sums of consecutive positive integers (2003) (1)
- Sums of squares of integers in arithmetic progression (2011) (1)
- Dirichlet’s Theorem on Primes in Arithmetical Progressions (1976) (1)
- Functions of number theory (2010) (1)
- Ode to andrew wiles, kbe (2000) (1)
- A Characteristic Property of the Mobius Function (1965) (1)
- Complete Dissections: Converting Regions and Their Boundaries (2011) (1)
- Identities for series of the type Σ()() (1973) (1)
- Volumes of solids swept tangentially around cylinders (2015) (1)
- New Horizons in Geometry: Unwrapping Curves from Cylinders and Cones (2012) (1)
- On the nonvanishing of homogeneous product sums (1986) (1)
- New Horizons in Geometry: Bibliography (2012) (1)
- Generalized Cyclogons (2002) (1)
- Asymptotic Series Related to the Partition Function (1951) (1)
- Ellipse to Hyperbola: “With This String I Thee Wed” (2011) (1)
- New Horizons in Geometry: Introduction (2012) (0)
- Beyond the Mechanical Universe (2008) (0)
- New Horizons in Geometry: Isoperimetric and Isoparametric Problems (2012) (0)
- THE CONSERVATION OF MOMENTUM (1986) (0)
- Visualization in Learning Mathematics with Hypervideo: The Story of Pi demo (2005) (0)
- EULER SUMS REVISITED (2003) (0)
- Elementary Problems: E2438-E2443 (1973) (0)
- Surprisingly Accurate Rational Approximations (2002) (0)
- THE APRIL MEETING IN BERKELEY The four hundred thirty-sixth meeting of the American Mathe - (2007) (0)
- The Mechanical Universe: ANGULAR MOMENTUM (1986) (0)
- The Mechanical Universe: THE INTERNATIONAL SYSTEM OF UNITS (1986) (0)
- New Horizons in Geometry: About the Authors (2012) (0)
- New Horizons in Geometry: Mamikon's Sweeping Tangent Theorem (2012) (0)
- A Glance at the World (2010) (0)
- New Horizons in Geometry: Preface (2012) (0)
- THE DECEMBER MEETING IN PASADENA The four hundred seventy-sixth meeting of the American (2007) (0)
- The Mechanical Universe: SOLVING THE KEPLER PROBLEM (1986) (0)
- New Horizons in Geometry: Appendix (2012) (0)
- Volumes of Solids Swept Tangentially Around General Surfaces (2015) (0)
- Summing the Initial Inverted Powers: 11128 (2007) (0)
- FORMULAS FROM ALGEBRA, GEOMETRY, AND TRIGONOMETRY (1986) (0)
- Calculus vol. 2 : multi-variabel calculus and linear algebra, with applications to differential equations and probability / Tom M. Apostol (1969) (0)
- New Horizons in Geometry: Trammels (2012) (0)
- Sines and Cosines. Part 3 of 3 (1992) (0)
- Periodic Arithmetical Functions and Gauss Sums (1976) (0)
- The Mechanical Universe: THE LAW OF FALLING BODIES (Program 2) (1986) (0)
- Congruences for the coefficients of the modular function j (1976) (0)
- Primitive character sums and Dirichlet L-functions† (1978) (0)
- New Horizons in Geometry: New Balancing Principles with Applications (2012) (0)
- Early History of Mathematics (2003) (0)
- Grassroots Democratic Activism in Altadena, California, in the Mid-Twentieth Century (2014) (0)
- Quadratic Residues and the Quadratic Reciprocity Law (1976) (0)
- THE QUEST FOR LOW TEMPERATURE (1986) (0)
- Good Rational Approximations to Logarithms (2001) (0)
- UNIVERSAL GRAVITATION AND CIRCULAR MOTION (1986) (0)
- Problems for Solution: 4473-4477 (1952) (0)
- Elliptic Dedekind-Rademacher Sums and Transformation Formulae of Certain Infinite Series (2019) (0)
- Index To Volume 120, 2013 (2013) (0)
- New Horizons in Geometry: Arclength and Tanvolutes (2012) (0)
- The Mechanical Universe: SELECTED BIBLIOGRAPHY (1986) (0)
- Index to the Mathematical Gazette (2006) (0)
- Linear Algebra (1997) (0)
- New Horizons in Geometry: Centroids (2012) (0)
- Problems for Solution: 4693-4697 (1956) (0)
- Problems for Solution: E1001-E1005 (1952) (0)
- New Horizons in Geometry: Cyclogons and Trochogons (2012) (0)
- KEPLER'S LAWS AND THE CONIC SECTIONS (Program 21) (1985) (0)
- THE APPROXIMATE FUNCTIONAL EQUATION OF (2016) (0)
- Arithmetical Functions and Dirichlet Multiplication (1976) (0)
- THE ENGINE OF NATURE (1986) (0)
- Volume/Surface Area Ratios for Globes, with Applications (2015) (0)
- New Horizons in Geometry: Cycloids and Trochoids (2012) (0)
- The Mechanical Universe: VECTORS (1986) (0)
- New Horizons in Geometry: Foreword (2012) (0)
- New Horizons in Geometry: Circumgons and Circumsolids (2012) (0)
- The Mechanical Universe: INTRODUCTION TO THE MECHANICAL UNIVERSE (Program 1) (1986) (0)
- THE JUNE MEETING IN EUGENE The four hundred eight-second meeting of the American Mathe- (2007) (0)
- New Horizons in Geometry: Ellipse to Hyperbola: “With This String I Thee Wed” (2012) (0)
- New Horizons in Geometry: New Descriptions of Conics via Twisted Cylinders, Focal Disks, and Directors (2012) (0)
- THE LANGUAGE OF NATURE: DERIVATIVES AND INTEGRALS (1986) (0)
- Triangles in Rectangles (1998) (0)
- The Tunnels of Samos (1995) (0)
- ANGULAR MOMENTUM (Program 19) (1985) (0)
- The Mechanical Universe: NEWTON'S LAWS AND EQUILIBRIUM (1986) (0)
- TEMPERATURE AND THE GAS LAWS (1986) (0)
- Dirichlet Series and Euler Products (1976) (0)
- FORCES IN ACCELERATING REFERENCE FRAMES (1986) (0)
- Video Based Hypermedia for Communicating Mathematics (2003) (0)
- Modular forms with multiplicative coefficients (1976) (0)
- The Functions ζ(s) and L(s, χ) (1976) (0)
- The Method of Punctured Containers (2007) (0)
- New Horizons in Geometry: Sums of Squares (2012) (0)
- Note on the trivial zeros of Dirichlet $L$-functions (1985) (0)
- Sums of consecutive positive integers (2003) (0)
- NAVIGATING IN SPACE (1986) (0)
- Topological Treatment of Platonic , Archimedean , and Related Polyhedra (2015) (0)
- New Horizons in Geometry: The Method of Punctured Containers (2012) (0)
- Finite Abelian Groups and Their Characters (1976) (0)
- A New Look at Surfaces of Constant Curvature (2016) (0)
- The Mechanical Universe: KEPLER'S LAWS AND THE CONIC SECTIONS (1986) (0)
- The Mechanical Universe: ROTATIONAL DYNAMICS FOR RIGID BODIES (1986) (0)

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