D. The Secondary School Mathematics Library: Its Collection and Use

Allendoerfer, C.B. , and Oakley, C. O. Principles of Mathematics. New York: McGraw-Hill Book Co. 1955. Introductory college text, assuming little background. Includes work on logic, the number system, groups, Boolean algebra, and introduces analytic geometry, calculus, statistics, and probability.

Anderson, Raymond W. Romping Through Mathematics. New York: Alfred A. Knopf. 1947. An interesting account of the story of mathematics through four thousand years.

Avis, F.C. Printers' Arithmetic. New York: Philosophical Library. 1956. Deals exclusively with the subject of type calculations, showing the methods by worked examples for over 30 kinds of problems.

Bakst, Aaron. Mathematical Puzzles and Pastimes. Princeton: D. Van Nostrand Co. 1954. A variety of problems for the math student, with emphasis on diversion.

. Mathematics; Its Magic and Mastery. Princeton: D. Van Nostrand Co. 1941. Designed for amusement, but not limited to the novel mathematical stunt. Develops mathematical processes and concepts through stories and amusing incidents.

Ball, W. W. Rouse. Mathematical Recreations and Essays. New York: Macmillan Co. 1947. A revision of useful edition in the field of recreations. Some chapters have been deleted, others added.

Banks, J. Houston. Elements of Mathematics. Boston: Allyn and Bacon. 1956. Begins at the beginning—"how we write numbers"—and builds up four broad aspects of elementary mathematics: number, proof, measurement, and functions. No knowledge of mathematics beyond elementary arithmetic is assumed. Good reading ability is necessary.

Begle, Edward G. Introductory Calculus. New York: Henry Holt. 1954.

Bell, Eric Temple. Mathematics; Queen and Servant of the Sciences. New York : McGraw-Hill Book Co. 1951. Designed to build an interest in mathematics and what mathematics can do. Narration touches on fields of mathematics with no attempt to be thorough, just to introduce.

_. Men of Mathematics. New York: Simon and Schuster. 1937. A collection of biographies of the great men of mathematics. Vivid accounts that bring the lives of these men into the view of the senior high-school reader.

Birkhoff, Garret. A Survey of Modern Algebra. New York: Macmillan Co. 1953. A college text, easily read, explaining the fundamentals of modern algebra, congruences, sets, classes, Boolean algebra.

Bonola, Robert. Non-Euclidean Geometry. New York: Dover Publications. 1955. For the teacher who wants to understand the hypotheses on which non-Euclidean geometry is based.

Boole, George. An Investigation of the Laws of Thought. New York : Dover Publications. 1951. A classic of pure mathematics and symbolic logic. The first extensive statement of the modern view that mathematics is a pure deductive science that can be applied to various situations.

Boyer, Lee Emerson. Introduction to Mathematics: A Historical Development. New York: Henry Holt and Co. 1955 . Designed for elementary- and secondary-school teachers, this book indicates "the nature, significance, and use of mathematics from early times to the present" with emphasis on practical applications.

Breslich, E.R. Excursion in Mathematics. Chicago: The Orthovis Co. 1938. Presents the use of common geometric figures in design, nature, and practical matters. Characteristics of the figures are noted and some of the measurement formulas are developed. Series of pictures to be viewed through the orthoscope accompanying the book.

_. Algebra, An Interesting Language. Chicago: The Orthovis Co. 1939.

Burington, Richard S., compiler. Handbook of Mathematical Tables and Formulas . Sandusky, Ohio: Handbook Pubs . 1948. Summary of formulas from algebra, geometry, and trigonometry. Rather complete tables.

Butler, Charles H. , and Wren, F. Lynwood. The Teaching of Secondary Mathematics. New York: McGraw-Hill Book Co. 1951 . A three part work: the place and function of mathematics in secondary mathematics; improvement and evaluation; teaching of special subject matter.

Cajori, Florian. A History of Elementary Mathematics. London: Macmillan Co. 1917. Evolution of the number signs, equal sign, exponents, etc. Vol. I: Symbols from elementary mathematics. Vol. II: Symbols from advanced mathematics.

Camp, Ezra John. Mathematical Analysis. Boston: D. C. Heath. 1956. For students who have had a year and a half of algebra. Introduces the idea of calculus early. Begins with coordinates, graphs, and functions.

Cooley, Hollis R. , et al. Introduction to Mathematics. Boston: Houghton Mifflin Co. 1949. The principal objectives include showing how mathematics builds theories which have wide applications in the physical, biological, and social sciences; the arts; and philosophy.

Coolidge, Julian Lowell. The Mathematics of Great Amateurs. New York: Oxford University Press. 1949. Biographies with emphasis on the mathematics of such persons as Durer, DaVinci, Pascal, Diderot.

Copi, Irving M. Introduction to Logic. New York: Macmillan Co. 1953. Elementary logic, presented in a manner that the superior high-school student can grasp.

Courant, Richard , and Robbins, Herbert. What Is Mathematics? An Elementary Approach to Ideas and Methods. New York: Oxford University Press. 1941. Not overlooking the formal aspects, this approach includes applications and connections of mathematics with other fields. Chapters on number theory, number system, geometric constructions, axiomatics and geometrics, topology, functions and limits may be read separately. Only high-school math is assumed.

Cundy, H. Martyn , and Rollett, A.P. Mathematical Models. New York: Oxford University Press. 1951. Models suitable for classroom or individual projects that illustrate abstract ideas in concrete form. Includes information on materials needed and the use of models.

Dadourian, H. M. How To Study : How To Solve. Cambridge, Mass.: Addison-Wesley Press. 1951. Covers arithmetic to calculus. General directions for studying are given, then specific ideas for solving a multitude of problem types.

Dantzig, Tobias. The Bequest of the Greeks. New York: Charles Scribner's Sons. 1955. A study of problems, principles, and procedures which modern mathematics has inherited from the Greeks.

. Number: The Language of Science. New York: Macmillan Co. 1954. A survey which the non-mathematician can grasp.

DeGrazia, Joseph. Math Is Fun. New York: Emerson Books . 1954. 196 puzzles, from elementary to intricate, including solutions.

Dixon, Wilfrid J. , and Massey, Frank J. Introduction to Statistical Analysis. New York: McGraw-Hill Book Co. 1951 . A textbook in statistics for students from all fields in which statistics finds application. Teachers will find useful.

Donaldson, Elvin F. Personal Finance. New York: Ronald Press Co. 1956. A rather complete work on credit, banks, life insurance, real estate, stocks, and bonds.

Dubisch, Roy. Nature of Number; An Approach to Basic Ideas of Modern Mathematics . New York: Ronald Press Co. 1952. A discussion of the ideas behind modem mathematics which concern the scientist today. For the teacher or the advanced student.

Dideney, Henry Ernest. Amusements in Mathematics. New York: Thomas Nelson and Sons. 1917. A very comprehensive collection of the traditional puzzles and recreations in mathematics.

Ewing, Claude H. , and Hart, Walter. Essential Vocational Mathematics. Boston: D. C. Heath and Co. 1945. Uses actual jobs of the vocational school shop in the illustrative examples.

Fraenkel, Abraham A. Integers and Theory of Numbers. New York: Scripta Mathematica, Yeshiva University. 1955 . A concise, easily read work on number theory. Good explanation of cardinal and ordinal.

Freeman, Mae B. , and Freeman, Ira. Fun with Figures. New York: Random House. 1946. Simple explanations and experiments designed to develop understanding of the characteristics and uses of common geometric figures. Well illustrated.

Friend, John A. N. Numbers, Fun, and Facts. New York: Charles Scribner's Sons. 1954.

Freund, John E. Modern Elementary Statistics. Englewood Cliffs, N. J.: Prentice-Hall. 1952. The only mathematical training assumed is algebra.

. A Modern Introduction to Mathematics. Englewood Cliffs, N. J.: Prentice-Hall. 1956. Requires no particular skill in algebra and geometry. Designed to develop an appreciation of mathematical thinking. Goes into number systems. Also Boolean algebra.

Gamow, G. Mr. Tompkins in Wonderland. New York: Cambridge University Press. 1957. Some important concepts of science and mathematics in an amusing setting. The humor of the work does not detract from its usefulness in presenting principles and at the same time will draw the younger reader.

Gardner, Randolph Scott. Instruments for the Enrichment of Secondary School Mathematics. Albany: Bookstore, New York State College for Teachers. 1951 . Each instrument is introduced by a historical study, followed by an explanation of mathematical theory and exercises.

Georges, Joel S. , et al. Preparatory Mathematics I. Ann Arbor: J. W. Edwards, Publisher. 1957. This book was designed as a textbook in a course for college freshmen who had had no algebra or geometry in high school. Whether or not it is useful for this purpose, it can be helpful in working with the high-school student who needs a review of these subjects.

Giiles, William F. The Magic and Oddities of Numbers. New York: Vantage Press. 1953. A collection of stunts from number nine to magic squares.

Hamilton, Walter T. Mathematical Analysis: A Modern Approach. New York : Harper and Bros. 1956. Presupposes preparation in elementary and intermediate algebra and plane geometry. Good for seniors. Designed to train students toward habits of independent research and analysis.

Hazard, William J. Algebra Notes. New York: Vantage Press. 1952. A collection of helps for the algebra student. Problems which many students have found difficult are solved—and diagrams are used as additional aids.

Hilbert, David. Geometry and the Imagination. New York: Chelsea Pub. Co. 1952. Attempts to present geometry in its visual, intuitive aspects. Treats many unusual facets.

Hills, E. J. A Course in the Slide Rule and Logarithms. Boston : Ginn and Co. 1950. Paper backed edition.

Hofmann, Joseph E. The History of Mathematics. New York: Philosophical Library, Inc. 1957. A good account of the period covering pre-Greek to 1650. Some detail on Middle Ages. Translated from the German. Too dry for most students.

Hogben, Lancelot Thomas. Mathematics for the Million. New York: W. W. Norton. 1951. Concerned not with classroom exercises but with practical use. Leads from simple arithmetic to calculus.

. Wonderful World of Mathematics. New York: Garden City Books. 1955. Non-technical for young readers. Color illustrations.

Holmes, Roger W. The Rhyme of Reason. New York: Appleton-Century-Crofts. 1939. An invitation to accurate and mature thinking. Twenty-five brain-teasers in appendix.

Hooper, Alfred. Arithmetic Refresher. New York: Henry Holt and Co. 1944. A review of arithmetic written for adults interspersed with history of arithmetic.

. Makers of Mathematics. New York: Random House. 1948. A short history of the men and ideas that formed the foundations of modern mathematics.

Horton, Halbrook Lynedon. Mathematics at Work. New York: Industrial Press. 1949. Practical applications of arithmetic, algebra, trigonometry, logarithms, and other math to engineering.

Huff, Darrell. How To Lie with Statistics. New York: W. W. Norton. 1954. A popular account and former best-seller for adults and students alike. Amusing, yet informative, about graphs, charts, and figures that can mislead.

Hunter, James A. H. Fun with Figures. New York: Oxford University Press. 1956. Hunter's own collection of brainteasers and math puzzles, most of which are short and modern in nature.

Hutchinson, Charles Angevine. Engineering Problems. New York: Harper and Bros. 1956. Mathematics with engineering applications.

Incorporated Association of Assistant Masters in Secondary Schools. The Teaching of Mathematics. New York : Cambridge University Press. 1957 . Gives syllabi for each year of the British secondary school, the teacher's philosophy, helps in teaching certain concepts, suggestions for the mathematics library, a description of the mathematics room, etc. American teachers can get many ideas and much help from a perusal of this work.

James, Glenn. Mathematics Dictionary. New York: D. Van Nostrand Co. 1949. An excellent work. Useful to help students clear up uncertain meanings and extend comprehension.

Johnson, Lee H. The Slide Rule. Princeton, N. J.: D. Van Nostrand Co. 1949. A complete book on the modern Duplex slide rule. A new method of operation is presented which makes full use of the versatility and efficiency of the Duplex rule. The treatment is progressive and self-teaching.

Jones, Burton W. The Theory of Numbers. New York: Rinehart and Co. 1955. The first three chapters are especially rich in material useful for secondary- and elementary-school teachers.

Jones, O.B. Applied Industrial Mathematics. Englewood Cliffs, N. J. : Prentice-Hall. 1947. Interweaves and applies the sciences of arithmetic, algebra, geometry, logarithms, trigonometry, physics, mechanics, and strength of materials in the solution of practical problems arising in manufacturing plants.

Jones, Samuel Isaac. Mathematical Clubs and Recreations. Nashville, Tenn.: S. I. Jones. 1940. Purpose, history, organization, aids, and aims of math clubs. Also contains a section on recreations with answers.

. Mathematical Nuts for Lovers of Mathematics. Nashville, Tenn.: S. I. Jones. 1932. Problems catalogued by age of solver, and where and by whom to be used.

_. Mathematical Wrinkles. Nashville, Tenn.: S. I. Jones. 1929. Numerous trick problems arranged by subject area. Chapters on quotations on math, organization of purpose of math clubs, and examination questions from certification tests.

Kasner, Edward , and Newman, James. Mathematics and the Imagination. New York: Simon and Schuster. 1940. A popular treatment of the important ideas of mathematics, ranging from the googol through geometries to calculus. The style is interesting, with unusual and humorous illustrations.

Kaufman, Gerald Lynton. Book of Modern Puzzles. New York: Dover Publications. 1956. Includes some reasoning problems using nonsense words.

Kells, Lyman M. Plane and Spherical Trigonometry. New York: McGraw-Hill Book Co. 1951.

Kemney, John G. ; Snell, J. Laurie ; and Thompson, Gerald L. Introduction to Finite Mathematics. Englewood Cliffs: Prentice-Hall. 1957. Designed to introduce advanced math students to some concepts in modem mathematics, with applications to the biological and social sciences. At least three years of math required. Valuable for teachers of secondary-school mathematics.

Kiely, Edmond R. Surveying Instruments; Their History and Classroom Use. New York: Columbia University Press. 1947. A complete history with practical exercises in outdoor measurement.

Kinney, Lucien B. , and Purdy, C. Richard. Teaching Mathematics in the Secondary School . New York: Rinehart and Co. 1952. Historical background of mathematics curriculum. Breaks problem into areas (i.e., algebra, geometry, general math). Discusses teaching aids and construction of tests.

Klein, Felix. Elementary Mathematics from an Advanced Standpoint. New York: Dover Publications, n.d. Using analytic formulas to accompany the space perceptions inherent in geometry, the author interprets and elucidates geometry. The teacher will find that it gives a comprehensive idea of the whole field of geometry.

Kline, Morris. Mathematics in Western Culture. New York: Oxford University Press. 1953. Relates mathematics to the culture in which it has developed. Makes interesting general reading.

Kramer, Edna E. The Mainstream of Mathematics. New York: Oxford University Press. 1951. Written in a narrative style and on a popular level, the mathematics, however, is valid and useful. The heavier concentration is on concepts of modern mathematics.

Langer, Susanne K. An Introduction to Symbolic Logic. New York: Dover Publications. 1956. An exhaustive work in this field. A great deal on classes, calculus of propositions, and logistics.

Larsen, Harold D. Arithmetic for Colleges. New York: Macmillan Co. 1950. A one-semester college course for students who plan to teach arithmetic. Much historical content.

Levi, Howard. Elements of Algebra. New York: Chelsea Pub. Co. 1956. Not the algebra of the traditional course. This small volume will be useful on the reading list of the teacher who hopes to teach more significant algebra to high-school students.

Lieber, Lillian R. The Education of T. C. Mits. New York: W. W. Norton and Co. 1942. What modern mathematics means to you. In a humorous style, Lieber takes the mystery from these matters. The best-known of Lieber's many.

. The Einstein Theory of Relativity. New York: Farrar and Rinehart. 1945. A clear and vivid exposition of the essentials, ideas, and methods of the theory of relativity; can be recommended especially to those who cannot spend too much time on the subject.

_. Infinity. New York: Rinehart and Co. 1953. An account of the role of the infinite in mathematics (great and small).

. Mits, Wits, and Logic. New York: Galois Institute Press. 1947. Formal logic in an informal style. How its study can be improved by the introduction of Boolean algebra, the algebra of sets and classes.

. Non-Euclidean Geometry. Brooklyn: Galois Institute of Mathematics and Art. 1940. Amusing light-hearted introduction to this modem subject. Presentation is careful and accurate.

_. Take a Number. New York: Ronald Press Co. 1946. Good reading for the general mathematics student. Written and illustrated in the Lieber style, it answers the perennial question, "Why study mathematics?"

Logsdon, Mayme L. A Mathematician Explains. Chicago: University of Chicago Press. 1935. The "what is it" of all the fields of mathematics, along with the "what for" and "how did it happen."

McKay, Herbert. Odd Numbers. New York: Macmillan Co. 1943. Uses "straight forward arithmetical processes, the simplest trigonometrical ratios, and a little elementary algebra" to present an amazing array of problem solutions. The student who has had a year of high-school mathematics can enjoy this book.

. The World of Numbers. New York: Macmillan Co. 1946. Numbers as used in geography and astronomy.

Manning, Henry Parker. Geometry of Four Dimensions. New York: Dover Publications. 1956. A popular treatment of the theory of the fourth dimension.

Mayor, John R. , and Wilcox, Marie S. Algebra, First Course. Englewood Cliffs, N. J.: Prentice-Hall. 1956 .

Menger, Karl. Calculus. Boston: Ginn and Co. 1955. One of the better of the recent calculus texts.

Meserve, Bruce E. Fundamental Concepts of Geometry. Cambridge, Mass. : Addison-Wesley Pub. Co. 1955 . Contains sections on projective, affine, Euclidean, non-Euclidean, geometry, and topology.

Meyer, Jerome S. Fun with Mathematics. New York: World Publishing Co. 1952. Easy to read explanations with illustrations drawn from common experience of fundamental mathematical principles such as numbers, powers, logarithms. Includes a chapter on making a good slide rule with an ordinary ruler. Good for the young reader.

Meyers, Lester. High-Speed Mathematics. New York: D. Van Nostrand Co. 1947. A whole book of short cuts and time-saving methods. Begins with the simplest processes of mental arithmetic and goes on through the various kinds of calculations used in business and industry.

Mira, Julio A. Mathematics of Finance. New York: D. Van Nostrand Co. 1954. For the student who is quite capable, this is a beginning text on mathematics of finance.

Mueller, Francis J. Arithmetic; Its Structure and Concepts. Englewood Cliffs, N. J.: Prentice-Hall. 1956 . Number, history of number, the synthesis and analysis of the operations, fractions, and approximate numbers.

National Council of Teachers of Mathematics. Emerging Practices in Mathematics. Washington 6, D. C.: The Council. 1954. Five parts: Various provisions for differentiated mathematics program; laboratory teaching in mathematics; teacher education; new emphases in subject matter; evaluation of mathematical education.

_. Insights Into Modern Mathematics. Washington 6, D. C.: The Council. 1957. Provides an introduction into several areas of modem mathematics for teachers of secondary mathematics who have had no opportunity to become acquainted with these developments.

. Multi-Sensory Aids in the Teaching of Mathematics. New York: Teachers College, Columbia University. 1945. A careful compilation of many of the different kinds of multisensory aids used in mathematics. Procedures used by many different successful teachers are included as well as descriptions of models and devices. There is an excellent bibliography.

Newman, James R. (ed). The World of Mathematics; A Small Library of the Literature of Mathematics from A'h-mose' the Scribe to Albert Einstein. 4 vols. New York: Simon and Schuster. 1956 . A compendium of mathematics in all its aspects. Numerous selections illuminate mathematics in its relation to its history and the world cultures to "pure thought" to the physical, biological, and social sciences to technology and art. Comments and essays of the editor furnish a unifying thread to this four-volume work. A recommended purchase for the larger school library.

Niven, Irvin M. Irrational Numbers. New York: John Wiley and Sons. 1956. Not an elementary text. Covers continued fractions, transcendental numbers.

Nodelman, Henry M. Mathematics for Electronics. New York: McGraw-Hill Book Co. 1956. College-level textbook relating mathematics to electronic engineering and engineering practice. Part III deals with the algebra of determinates. Part VI gives the elements of Boolean algebra and includes material on switching circuits.

Northrop, Eugene P. Riddles in Mathematics; A Book of Paradoxes. Princeton : D. Van Nostrand Co. 1944. "Devoted exclusively to some of the paradoxes which mathematicians, both amateur and professional, have found disconcerting." Popular treatment.

Ogilvy, C. Stanley. Through the Mathescope. New York: Oxford University Press. 1956. Popular discussion of selected topics concerning number theory, algebra, geometry, and analysis for the advanced student.

Olivo, C. Thomas. Basic Mathematics Simplified. Albany: Delmar Publica. tions. 1953. Uses illustrations from the fields of industrial and vocational education. General mathematics level.

Ore, Oystein. Neils Henrik Abel , Mathematician Extraordinary. Minneapolis: University of Minnesota Press. 1957. An interesting description of the life of one of the latter-day mathematicians. Of interest to students due to the amount of math contributed in a short lifetime (26 years).

. Number Theory and Its History. New York: McGraw-Hill Book Co. 1948. An excellently written college text.

Peters, Max. Going Places with Mathematics. Englewood, N. J. : Prentice-Hall. 1956. Actually a general mathematics text written using a fictional family as they meet mathematical situations.

Polya, G. How To Solve It; A New Aspect of Mathematical Method. Princeton: Princeton University Press. 1945. Methods of solution useful to teachers of mathematics and anyone else "concerned with the ways and means of invention and discovery." May be difficult for most high-school students.

_. Mathematics and Plausible Reasoning. Princeton: Princeton University Press. 1954. Volume I—Induction and Analogy in Math; Volume II—Patterns of Plausible Inference.

Primrose, E.J.F. Plane Algebraic Curves. London: Macmillan Co., n.d. Elementary curves. The study is intended for college undergraduates, but good high-school seniors could study the first few chapters with profit.

Quine, Willard Van Orman. Mathematical Logic. Cambridge, Mass.: Harvard University Press. 1955. This work requires no previous knowledge of logic or higher mathematics. It is a very rigorous presentation, however, and only the gifted and serious high-school student should attempt it. Teachers will find it useful.

Rademacher, Hans , and Toeplitz, Otto. The Enjoyment of Mathematics; Selections from Mathematics for the Amateur . Princeton: Princeton University Press. 1957. Intended to extend the enjoyment of mathematics for those who are gifted to all who will take the time. Only a year each of algebra and geometry will be needed for background.

Ravielli, Anthony. Adventure in Geometry. New York: Viking Press. 1957. A very well-illustrated text dealing with basic definitions of plane and solid geometry. Some of the more interesting curves are illustrated. Some work on projective geometry.

Reichmann, W.J. The Fascination of Numbers. Fair Lawn, N. J.: Essential Books, Inc. 1957. This work is largely devoted to a presentation of the fundamental aspects of number theory. Most students who have had two years of high-school mathematics can make good use of this part. There are also some recreational chapters which anyone who likes numbers can enjoy.

Reid, Constance. From Zero to Infinity; What Makes Numbers Interesting. New York: Thomas Y. Crowell Co. 1955. A popular discussion in which a chapter is devoted to each of the numbers, 0 through 9, and infinity. History, number theory, and recreations are well blended.

Richards, Richard Kohler. Arithmetic Operations in Digital Computers. New York: D. Van Nostrand Co. 1955. Contains material on Boolean algebra as applied to computer operations and arithmetic of the binary system. Explains programming.

Roberts, Helen M. , and Stockton, Doris S. Elements of Mathematics. Reading, Mass.: Addison-Wesley Publishing Co. 1956. A basic review of secondary-school algebra.

Sanford, Vera. A Short History of Mathematics. New York: Houghton-Mifflin Co. 1930. Source for historical information. Concerned more with the ancient and medieval development of mathematics than with the advanced and modem development.

Shackle, G.L.S. Mathematics at the Fireside; Some Fundamentals Presented to Children . New York: Cambridge University Press. 1952. For the young, the conversational approach informally covers the development of the number concept and some of the elemental ideas of analytical geometry, the calculus, and algebra.

Shupe, Hollie W. A Manual of Engineering Geometry and Graphics for Students and Draftsmen . New York: McGraw-Hill Book Co. 1956 . A mechanical drawing text, but contains many practical applications for intuitive geometry.

Slade, Samuel. Mathematics for Technical and Vocational Schools. New York : J. Wiley and Sons. 1936 . A textbook covering the simple, practical mathematics needed in the shop. Contains work on the slide rule, trigonometry, graphs, and logarithms.

Spitzer, Herbert F. Practical Classroom Procedures for Enriching Arithmetic. St. Louis: Webster Publishing Co. 1956. A whole book of ideas and exercises which teachers can use to make arithmetic more enjoyable and to help students toward a quicker and more thorough understanding of concepts.

Staler, Edward R. An Introduction to Mathematical Thought. Cambridge, Mass. : Addison-Wesley Publishing Co. 1953. The nature of mathematics, logic, and an axiomatic system with examples from elementary algebra and geometry together with an introduction to the axioms for a field and to Boolean algebra.

Steinhaus, Hugo. Mathematical Snapshots. New York: Oxford University Press. 1950. Problems and tricks in mathematics, wonderfully and clearly illustrated, and prepared for the reader with only a year of high-school algebra.

Struik, Dirk J. A Concise History of Mathematics. New York: Dover Publications. 1948. Unfolds the main ideas in the development of mathematics up to 1900.

Swain, Robert L. Uunderstanding Arithmetic. New York: Rinehart and Co. 1957. An exhaustive work on number theory directed toward elementary teachers, but could be understood by students. Covers the four operations, other bases, some set theory. Many teaching aids and problems. Actually a text.

Underwood, Ralph S. , and Sparks, Fred. Living Mathematics. New York: McGraw-Hill Book Co. 1949. A first-year college text which contains ideas, comments, and illustrations which build interest.

Vance, Elbridge P. Unified Algebra and Trigonometry. Cambridge, Mass. : Addison-Wesley. 1955. Progresses rapidly from simple algebra to more complex which is then intermixed with trigonometry. The senior trigonometry student should profit from a study of this book.

Wade, Thomas Leonard. Fundamental Mathematics. New York: McGraw-Hill Book Co. 1956. For first-year college students who do not have the preparation for the usual first-year courses. High-school seniors who feel a lack in their background can make profitable use of this book.

Weerden, Bartel Leendert van der. Science Awakening. New York : Stechert-Hafner, 31 E. Tenth St. 1954. Actually a history of mathematics from Egyptians to the decay of the Greek mathematic.

Weeks, Raymond. Boys' Own Arithmetic. New York: E. P. Dutton and Co. 1924. A humorous book made up of stories containing arithmetic problems. Good for general mathematics students.

Weyl, Hermann. Symmetry. Princeton: Princeton University Press. 1952. An excellent exposition, written by a master, ranging from simple mathematical aspects of artistic ornament to deep results in group theory.

Whitehead, Alfred North. An Introduction to Mathematics New York: Oxford University Press. 1948. A model of popular, but not over-simplified, exposition. Well worth reading.

Wilder, Raymond L. Introduction to the Foundations of Mathematics. New York : John Wiley and Sons. 1952. Suitable as a text for a college course in the subject. Explains some of the current problems in the foundations of mathematics and outlines the tenets of the principal "schools." Some of the material is intrinsically very difficult.

Wilson, Wallace A. Analytic Geometry. Boston: D. C. Heath and Co. 1925. A standard college text.