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Current Textbook List
(Approved 3/20/06 by UPC) |
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Course |
Current Textbook |
Topics to be covered |
Suggested Resources for the
Instructor |
| 165 |
Calculus 1 |
James Stewart-Calculus
Early Transcendentals (5th), Brooks/Cole, 2003. |
Chapters
1 through 5. Chapter 1 may be taught at the beginning, or its content may be
introduced as needed in the subsequent chapters. Sections 3.9 and 5.6 are
optional. Sections 3.3 and 4.8 need not be covered in their entirety, but
some applications from these sections should be treated. |
Mathematica
Tutorial and Sample Labs |
| 166 |
Calculus 2 |
James Stewart-Calculus
Early Transcendentals (5th), Brooks/Cole, 2003. |
Course
includes a brief review of Chapter 5, and portions of Chapters 6, 7, 8, 11,
10, and 9. Sections 8.3, 8.4, and 8.5 need not be covered in their entirety,
but some applications should be treated. Sections 11.11, 10.5, and 10.6
should be omitted. In Chapter 9, sections 9.3 and 9.4 should be covered and
the other sections are optional. |
Mathematica
Tutorial and Sample Labs |
| 215 |
Discrete Systems |
Kenneth H. Rosen-Discrete Mathematics and its Applications (5th), McGraw-Hill. |
Chapters 1-8, with some sections
omitted at the discretion of the instructor.
Instructors may need to supplement the material on number systems. |
|
| 217 |
Linear Algebra |
David C. Lay, Linear Algebra and its Applications
(3rd, updated), Addison-Wesley, 2005. |
Core sections are sections
1.1-1.9, 2.1-2.3, 3.1-3.3, 4.1-4.7, 5.1-5.4, 6.1-6.3, 6.5, and 7.1.
Several applications should also be included and may be chosen from sections
1.10, 2.6, 2.7, 4.8, 4.9, 5.6, 5.7, 6.6, and 7.5. As time allows, advanced
topics, selected from sections 2.5, 5.5, 6.4, 6.7, 6.8, 7.2, 7.3, and 7.4,
should be included. |
Mathematica
Tutorial and Sample Labs |
| 267 |
Calculus 3 |
James Stewart-Calculus
Early Transcendentals (5th), Brooks/Cole, 2003. |
Chapters
12, 13, 14, 15, and 16. The required portion of Chapter 13 consists of
sections 13.1, 13.2, and the portion of 13.3 treating arc length. The
remainder of Chapter 13 is optional, and should be saved until the end of the
course. |
Mathematica
Tutorial and Sample Labs |
| 271 |
Math Contest Problem Solving |
No Text |
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| 298 |
Undergraduate Colloquium |
No Text |
|
|
| 299X |
Experimental/ Developmental
Topics |
To be arranged. |
Topics and textbook will vary. |
|
| 311 |
Algebraic Structures |
Thomas Hungerford, Abstract Algebra: An Introduction (2nd),
Saunders College Publishing/Harcourt Brace. |
Chapters 1-4, parts of chapters 5 and 6,
first half of chapter 7. |
|
| 320 |
Probability |
Hogg and Tanis-Probabilty and Statistical Inference
(7th), Prentice Hall. |
|
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| 321 |
Mathematical Statistics |
Hogg and Tanis-Probabilty and Statistical Inference
(7th), Prentice Hall. |
|
|
| 335 |
Mathematical Models |
Douglas Mooney and Randall
Swift-A Course in Mathematical Modeling, Mathematical Association of America. |
|
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| 345 |
Survey of Geometries |
Michael Henle-Modern
Geometries-Non-Euclidean, Projective and Discrete
(2cd), Prentice Hall. |
The core of the course material
is chapters 1 through 10 of Henle. It
may be necessary to use other sources to cover the classical theorems of
Euclidean geometry. |
Geometer's
Sketchpad and Mathematica may be used.
Wallace, E.C & West, S. F., Roads to Geometry (2nd); Perry, E.,
Geometry: Axiomatic Developments with Problem Solving; Eves, H., College Geometry; Thomas, D.,
Modern Geometry; Blair, David E., Inversion Theory and Conformal Mapping;
Coxeter, H. S. M., Introduction to Geometry (2nd); Faber, Richard L.,
Foundations of Euclidean and Non-Euclidean, Geometry; Feeman, Timothy G.,
Portraits of the Earth: A Mathematician Looks at Maps; Jennings, George A.,
Modern Geometry with Applications. |
| 351 |
Mathematics of Finance |
Steven Kellison-The Theory of Interest (2cd),
McGraw-Hill/Irwin, 1991. |
The syllabus for the second
actuarial exam includes most of Chapters 1-8 of this book.
|
Mathematics of Investment and
Credit by Broverman; The Theory of Interest and Life Contingencies with
Pension Applications by Parmenter. |
| 355 |
Problems in Actuarial Science |
Samuel A. Broverman, ACTEX Study Manuel for the SOA/CAS Course 1 Examination, (2005 edition), ACTEX Publishing. |
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| 362 |
Numerical Analysis 1 |
Ward Cheney, David Kincaid, Numerical Mathematics and Computing
(5th), Brooks/Cole. |
Chapters 1-10, 12 |
Atkinson, An Introduction to
Numerical Analysis, (2nd); Burden and Faires, Numerical Analysis (7th);
Issacson and Keller, Analysis of Numerical Methods; Lindfield and Penny,
Numerical Methods Using Matlab (2nd); Van Loan, Introduction to Scientific
Computing (2nd) |
| 363 |
Numerical Analysis 2 |
Ward Cheney, David Kincaid, Numerical Mathematics and Computing
(5th), Brooks/Cole. |
Chapters 11, 13-17 |
Atkinson, An Introduction to
Numerical Analysis, (2nd); Burden and Faires, Numerical Analysis (7th);
Issacson and Keller, Analysis of Numerical Methods; Bau and Trefethen,
Numerical Linear Algebra; Varga, Matrix Iterative Analysis |
| 368 |
Unpaid Professional Experience in
Mathematical Sciences |
No Text |
|
|
| 369 |
Paid Professional Experience in
Mathematical Sciences |
No Text |
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| 374 |
Differential Equations |
Boyce and Diprima-Elementary Differential Equations and Boundary Value Problems (8th), Wiley, 2005. |
Chapters 1, 2, 3, 4, 6.1, 6.2,
and 7 form the core material. The rest
of the course is at the discretion of the instructor. Possible topics: Chapters 6.3-6.6 (Laplace Transform in more
detail); 5 (Power Series solutions); 8 (Numerical Methods); 9 (Nonlinear
Differential Equations and Stability). |
Elementary Differential
Equations (8th ed) by
Rainville, Rainville, and Bedient; Differential Equations and Boundary Value
Problems, Computing and Modeling, by Edwards and Penny, Differential
Equations with Boundary Value Problems (4th ed), by Zill and Cullen |
| 377 |
Complex Analysis |
James Ward Brown and Ruell V.
Churchill-Complex Analysis (7th),
McGraw-Hill. |
The course material is contained
in Chapters 1 through 9. |
|
| 390 |
Honors Colloquium in Mathematics |
To be arranged. |
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| 411 |
Abstract Algebra 1 |
John B. Fraleigh, A First Course in Abstract Algebra
(7th), Addison-Wesley, 2002. |
Chapters
0-17,34-40. |
David
S. Dummit & Richard M. Foote, Abstract Algebra (2nd). Portions of Chapters 1-6. |
| 412 |
Abstract Algebra 2 |
John B. Fraleigh, A First Course in Abstract Algebra
(7th), Addison-Wesley, 2002. |
Chapters
18-33,45-56. |
David
S. Dummit & Richard M. Foote, Abstract Algebra (2nd). Portions of Chapters 7-9, 13-14. |
| 415 |
Applications of Discrete
Mathematics |
Michaels and Rosen-Applications in Discrete Mathematics,
McGraw-Hill Science/Engineering/Math, 1991. |
Topics will vary. |
|
| 416 |
Theory of Numbers |
Kenneth H. Rosen, Elementary Number Theory and its Applications (5th), Addison Wesley. |
|
David M. Burton, Elementary
Number Theory. |
| 422 |
Theory of Sampling and Surveys |
Cochran, William G., Sampling Techniques (3rd), Wiley,
1977. |
|
Cochran, William G., Sampling Techniques (3rd);
Sukhatme, P. V., Sukhatme, B. V., Sukhatme, S., and Asok, C., Sampling Theory of Surveys with
Applications; Valliant, R., Dorfman, A. H., and Royal, R. M., Finite Population Sampling and Inference: A
Prediction Approach; Lohr, S.
Sampling: Design and Analysis, Duxbury Press, Pacific Grove, 1999;
Kish, Leslie Survey Sampling, Second Printing, John Wiley and Sons, Inc.,
1965. |
| 428 |
Regression and Time Series Models |
Bruce L. Bowerman, Richard
O’Connell, and Anne Koehler, Forecasting, Time Series
and Regression (4th), Duxbury, 2004. |
|
Miller, Robert B. and Wichern,
Dean W., Intermediate Business
Statistics: Analysis of Variance, Regression, and Time Series; Mendenhall,
William and Sinchich, Terry, A Second Course in Business Statistics (5th);
Robert S. Pindyck and Daniel Rubenfeld, Economic Models and Economic
Forecasts (4th), McGraw-Hill; Abraham, Bovas and Ledolter, Introduction to
Regression Modeling, Duxbury. |
| 429 |
Analysis of Variance in
Experimental Design Models |
Douglas C. Montgomery, Design and Analysis of
Experiments (6th), John Wiley & Sons, 2004. |
|
Graybill, Franklin A., Theory
and Application of the Linear Model. ; John, Peter W. M., Statistical Design
and Analysis of Experiments; Leik, Robert K., Experimental Design and
Analysis of Variance. |
| 441 |
Geometry and Topology |
Stephen C. Carlson-Topology of Surfaces, Knots, and Manifolds: A First Undergraduate
Course, Wiley; I.S.ed edition, 2001. |
This text will serve for a basic
introduction to topology. However,
some selected topics might be treated in more depth than suggested in this
text. |
|
| 445 |
Differential Geometry |
Barrett O'Neill, Elementary Differential Geometry (2nd),
Academic Press, 1997. |
|
Manfredo
do Carmo, Differential Geometry of Curves and Surfaces; Alfred Gray, Modern
Differential Geometry of Curves and Surfaces with Mathematica, (2nd). |
| 452 |
Mathematics of Life Contingencies
1 |
Bowers, Gerber, Hickman, Jones,
and Nesbitt, Actuarial Mathematics
(2cd), Society of Actuaries, 1997. |
The syllabus for the third
actuarial exam includes most of Chapters 3-10 of this book. |
Life Contingencies, by Jordan,
and The Theory of Interest and Life Contingencies with Pension Applications,
by Parmenter. |
| 453 |
Mathematics of Life Contingencies
2 |
Bowers, Gerber, Hickman, Jones,
and Nesbitt, Actuarial Mathematics
(2cd), Society of Actuaries, 1997. |
The syllabus for the third
actuarial exam includes most of Chapters 3-10 of this book. |
Life Contingencies, by Jordan,
and The Theory of Interest and Life Contingencies with Pension Applications,
by Parmenter. |
| 454 |
Mathematics of Investments |
Zvi Bodie, Alex Kane, and Alan
J. Marcus, Investments (6th),
McGraw Hill/Irwin. |
|
The Handbook of Fixed Income
Securities by Frank J. Fabozzi. |
| 456 |
Introduction to Operations
Research |
Hiller and Lieberman, Introduction to Operations Research
(8th), McGraw-Hill. |
Chapters 1 (Introduction); 3, 4,
5, 6.1-6.4 (Linear Programming); 8, 9 (Transportation and Network); 11.1,
11.3 (Dynamic Programming); 11
(Integer Programming); 12 (Optimal Nonlinear Programming) |
Winston, Operations Research
(3rd); Ecker and Kupferschmid, Introduction to Operations Research
|
| 457 |
Loss Distributions |
Klugman, S.A., Panjer, H.H. and
Willmot, G.E, Loss Models: From Data to Decisions, (2cd), 2004. Course 3
Study Note No. 3-23-02, and Credibility Study Note No. 4-21-01. (Both study notes, if available, are
downloadable from the Society's web site - www.soa.org.) |
|
Klugman, S.A., Panjer, H.H. and
Willmot, G.E, Loss Models: From Data to Decisions, (2cd), 2004, Foundations
of Casualty Actuarial Science (4th), Chapter 8, "Credibility", by
Mahler, H.C., and Dean C.G., (available as SN C-21-01); Topics in Credibility Theory by Dean, C.G., (Study Note C-24-05) |
| 458 |
Practicum in Actuarial Science |
No Text |
Because the topics of the
practicum change annually, the course has no pre-assigned text. Participating actuaries may require course
reading for their individual segments. |
|
| 460 |
History of Mathematics |
D. Burton, The History of
Mathematics (5th), McGraw-Hill Science/Engineering/Math, 2002. |
|
Victor Katz, A History of
Mathematics: An Introduction (2cd), Addison Wesley, 1998; C. Boyer, A History
of Mathematics (2cd); R. Calinger, Classics of Mathematics; R. Calinger, A
Contextual History of Mathematics; W. Dunham, Journey Through Genius; Euclid,
The Thirteen Books of Euclid's Elements, Translated with commentary by Sir
Thomas Heath; H. Eves, An Introduction to the History of Mathematics (5th);
M. Kline, Mathematical Thought from Ancient to Modern Times; D. Struik (Ed.),
A Source Book in Mathematics 1200-1800. |
| 465 |
Computational Techniques of
Financial Mathematics |
John C. Hull, Options, Futures, and Other Derivative Securities (6th), Prentice Hall, 2005. |
Chapters 1-14
and 16-17, with emphasis on Chapter 14. |
|
| 471 |
Real Analysis 1 |
Rudin-Principles
of Mathematical Analysis (3rd), McGraw-Hill, 1976. |
Chapters 1, 2, 3 (part), 4, 5, 9
(part). |
Tom M. Apostol, Mathematical
Analysis (2nd) (Chapters 1, 3, 4, 5, 12, and Chapter 2, 2.10-2.15); R.
Creighton Buck, Advanced Calculus (3rd) (Chapters 1, 2, 3, 7 (part)); Steven
A. Douglass, Introduction to Mathematical Analysis (Chapters 1, 2, 3, 4, 8). |
| 472 |
Real Analysis 2 |
Rudin-Principles
of Mathematical Analysis (3rd), McGraw-Hill. |
Chapters 3 (part),6,7,9
(part),10 (part). |
Tom M. Apostol, Mathematical
Analysis (2nd) (Chapters 6, 7, 8, 9, 13, 14); R. Creighton Buck, Advanced
Calculus (3rd) (Chapters 4, 5, 6, 7 (part), 8); Steven A. Douglass,
Introduction to Mathematical Analysis, (Chapters 5, 6, 7, 9, 10, 11, 12). |
| 473 |
Boundary Value Problems |
David Powers, Boundary
Value Problems (5th), Elsevier, 2006. |
A review of ordinary
differential equations is included as Chapter 0. The core material is Chapters 1-5. Additional topics at the discretion of the
instructor may be found in the text. |
Fourier Series, by G. P.
Tolstov; Applied Partial Differential Equations with Fourier Series and
Boundary Value Problems (4th ed) by Richard Haberman, Partial Differential
Equations and Boundary Value Problems with Maple V by George A. Articolo, and
Fourier Series and Boundary Value Problems, by R.V. Churchill. |
| 475 |
Topics in Partial Differential
Equations |
Kythe, Puri, Schafferkotter, Partial Differential Equations and Boundary Value Problems with
Mathematica (2cd) |
Chapters 1, 2, 4 and 5 (cover
briefly), 6 (part I), 7. |
Partial Differential Equations
and Mathematica, by Dimitri Vvedensky; Partial Differential Equations,
Methods and Applications by Robert McOwen; Introduction to Partial
Differential Equations by Donald Greenspan; Applied Partial Differential
Equations with Fourier Series and Boundary Value Problems (4th) by Richard
Haberman; Partial Differential Equations, Sources and Solutions by Arthur
David Snider; Partial Differential Equations by Walter Strauss; Introduction
to Partial Differential Equations with Applications by E. C. Zachmanoglou and
Dale W. Thoe; Partial Differential Equations by Fritz John; Partial
Differential Equations, Analytical Solution Techniques (2cd) by J. Kevorkian. |
| 497 |
Student-Faculty Colloquium |
To be arranged. |
Topics and textbook will vary. |
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| 498 |
Senior Seminar |
To be arranged. |
Topics and textbook will vary. |
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| 499 |
Reading and Honors |
To be arranged. |
Topics and textbook will vary. |
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