A generally accepted origin of the word ‘Mathematics’ is attributed to the Greek, μάθημα meaning lesson or a unit of study.
The Academic Press Dictionary of Science and Technology defined Mathematics as a “study of quantities, their relationships, operations and measurements expressed by numbers and symbols”.
Salomon Bochner, an American Mathematician, considered Mathematics as the language of Science and “an indispensable medium by which and within which Science expresses, formulates, continues and communicates itself”. It has been said that the grammar of this language is guided by rules of logic and its vocabulary comprises of symbols.
The history of Mathematics goes back to more than 5,000 years and one of oldest known mathematical implement, dated to about 30,000 BCE, is a wolf bone on which tally marks were carved. Mathematics in ancient Egypt and Babylon consisted mainly of Arithmetic while the ancient Greeks were engrossed with Geometry. In his book, The Language of Mathematics, Keith Devlin noted that in 1900, Mathematics consisted of about 12 distinct subjects (including arithmetic, geometry and calculus). Before the end of the 20th century, it has grown to more than 60 distinct categories.
Mathematics curriculum in numerous universities offers mainly two tracks of study, ‘Pure Mathematics’ and ‘Applied Mathematics’. The former is a study of mathematical theory and structures “without any necessary reference to their respective physical applications in the real world”. The latter, ‘Applied Mathematics’ can be described as the study of the mathematical techniques to solve practical problems.
The Division of Mathematical Sciences (MAS) in NTU’s School of Mathematics and Physical Sciences offer a variety of B.Sc programmes, including a double degree in Mathematics and Economics.
Graduates have entered the workforce as financial analyst/planner, investment analyst, biostatistician, software engineer, systems analyst, just to name a few.
Although there isn’t a Nobel Prize in Mathematics, there are a number of prizes awarded to mathematicians in recognition of their contributions to the field. Some of these prestigious awards are:
- Abel Prize This was first awarded by the Norwegian Academy of Science and Letters in 2003. The 2012 Laureate is Endre Szemeredi for his fundamental contributions to discrete mathematics and theoretical computer science, and in recognition of the profound and lasting impact of these contributions on additive number theory and ergodic theory..
- Fields Medal This is awarded by the International Mathematical Union (IMU) every 4 years to mathematicians under age 40. The 2010 recipients were Elon Lindenstrauss, Ngô Bảo Châu, Stanislav Smirnov, and Cédric Villani.
- Wolf Prize in Mathematics The 2010 recipients were Shing-Tung Yau in recognition for his work in geometric analysis and Dennis Sullivan for his innovative contributions to algebraic topology and conformal dynamics.
Real analysis, often called mathematical analysis or simply analysis, may be regarded as a formidable counterpart of calculus. Some good sources on real analysis are provided in this guide.read more
Linear algebra is the branch of mathematics on studying of the problem of solving systems of liner question. The application of it may be found in natural sciences, economics, and computers science. The resources listed in this guide are mainly for undergraduate students to acquire some solid foundation and appreciation of the field.read more
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Books provide good sources of information; from those explaining fundamental concepts suitable for students to in-depth specialized information suitable for research. You can find most of the books related to Mathematics in the Lee Wee Nam Library Science Collection. Titles related to Statistics and Mathematical Economics are shelved in the Business Library and HSS Library.
I want to first highlight a few useful textbooks found in the library collection.
- Undergraduate Texts in Mathematics (Springer)
- Graduate Texts in Mathematics (Springer)
- Wiley Series in Probability and Statistics (Wiley)
- Discrete Mathematics and its Applications (Chapman & Hall / CRC Press)
- Lecture Notes in Mathematics (Springer)
- Lecture Notes in Statistics (Springer)
- Lecture Notes in Pure and Applied Mathematics (Dekker)
Browsing the Collection
NTU Library books (print) are classified and shelved according to the Library of Congress (LC) classification numbers. Books on Mathematics generally are assigned with call numbers starting with QA. Listed below are some categories of mathematics and their corresponding broad class numbers.
|Mathematical economics||HB135 – 147|
|Business mathematics||HF5691 – 5716|
|Probabilities||QA273 – 274|
|Mathematical statistics||QA276 – 280|
|Numerical analysis||QA297 – 299.4|
|Geometry||QA440 – 699|
LC Classification List for Mathematical Sciences
Searching for Books
When looking for books under a specific subject category, you may use appropriate subject terms in the SUBJECT field when you search the Library Catalogue. As the books are arranged according to their call numbers, do take note of their respective call numbers and holding locations for ease of access. The latest editions of recommended texts and references are shelved in the Reserves collection.
Selected Books by Subjects
- Linear Algebra
- Abstract Algebra
- Number Theory
- Combinatorial Analysis
- Proof Theory
- Partial Differential Equations
- Functions of Real Variables
Staff and students can recommend book titles to the library for acquisition. Staff can recommend through StaffLink as follows: Resource Request — Library Services — Book Recommendation. Students can send an e-mail to email@example.com with the following details: Title, Author/Editor, Place of publication, Publisher or producer, Date of publication, ISBN and Edition, Price. For more details, please refer to New Title Recommendation.
The great thing about e-books is that they can be accessed remotely, anytime, anywhere. There are 4 major e-book collections for Mathematics. Take a look.
Enter Springerlink and look for ‘Mathematics and Statistics’ under Browse By collection. Next, filter by ‘books’ or ‘book series’.
Notable series include:
- Springer Undergraduate Mathematics Series “The Springer Undergraduate Mathematics Series (SUMS) is a series designed for undergraduates in mathematics and the sciences worldwide. From core foundational material to final year topics, SUMS books take a fresh and modern approach. Textual explanations are supported by a wealth of examples, problems and fully-worked solutions, with particular attention paid to universal areas of difficulty. These practical and concise texts are designed for a one- or two-semester course but the self-study approach makes them ideal for independent use.” [As taken from Springer]
- Undergraduate Texts in Mathematics“Undergraduate Texts in Mathematics provide introductions to the diverse sub-fields of mathematics. Generally aimed at third- and fourth-year undergraduate mathematics students at American universities, these texts often provide both students and teachers with new perspectives on the material. Even for standard topics of the undergraduate curriculum, most of these books provide novel approaches and insights. As effective tools for teaching, the books include motivation to guide the reader to see the internal connections of the subject, examples to show the concrete manifestations of the concepts, and many exercises at all levels of difficulty to test and strengthen understanding.” [As taken from Springer]
- Lecture Notes in Mathematics“This series reports on new developments in all areas of mathematics and their applications quickly, informally and at a high level.” [As taken from Springer]
- Universitext“Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, to very polished texts.” [As taken from Springer]
- Graduate Texts in Mathematics“Designed to bridge the gap between passive study and creative understanding, this series offers advanced-level introductions to current research. The volumes are carefully written as teaching aids and highlight characteristic features of the theory. They are often used as texts, and, in fact, most frequently their audience consists of the teachers and students of graduate courses in mathematics; they are, however, not only course books but are suitable for individual study as well.” [As taken from Springer]
Enter CRCnetBASE. Browse by Content, Subject ->‘Math’ or ’Statistics’and filter by ‘books’ or ‘book series’. View its Database Information Page.
The collection provides an online library of top-tier Chapman & Hall/CRC references, handbooks, pocketbooks, and primers.
Over 400 online titles now available in the areas of:
Algebra, Algebraic Geometry & Number Theory, Applied Mathematics, Combinatorics & Discrete Mathematics, Differential Equations & Nonlinearity, General Mathematics & Introductory Mathematics, Geometry & Topology, Mathematics for Biology & Medicine, Mathematical Modeling, Mathematics for Engineering, Mathematics for Finance, Mathematics for Physics, Numerical Analysis & Mathematical Computation, Operations Research, Probability Theory & Applications, Real, Complex & Functional Analysis and Set Theory & Logic. View its Database Information Page.
This collection meets the needs of statisticians and researchers employing statistical science across a wide range of disciplines. From Frequentist to Bayesian, biostatistics to finance, this fully searchable collection is the perfect tool for any size analysis on all sorts of data.
Over 300 online titles now available in the areas of:
Biostatistics, clinical Trial, Computational Statistics, Environmental Statistics, Introductory Statistics & General References, Probability Theory & Applications, SPC/Reliability/Quality Control, Statistical Genetics & Bioinformatics, Statistical Learning & Data Mining, Statistical Theory & Methods, Statistics for Biological Sciences, Statistics for Business, Finance, & Economics, Statistics for Engineering and Physical Science, Statistics for Psychology and Social Science & Law. View its Database Information Page.
Literature guides, dictionaries, encyclopaedias and handbooks are some works that serve as quick references and authoritative sources of information. Some reference works focus on specific applications of mathematics for example the ‘Number Theory’ and ‘Combinatorics’, while others cover broad areas of the subject.
The titles below is a small selection of resources (both print and electronic) available in the Library collection. You can search for other reference works on the Library Catalogue using appropriate search terms. Do refer to Search Tips provided in the FAQs.
Content at a Glance
Guides to the Mathematics Literature
These works are useful sources of information for Mathematics librarians, students and Mathematicians. A typical guide usually includes subject bibliographies of recommended books in some disciplines of Mathematics.
- Guide to Information Sources in Mathematics and Statistics. By Martha A. Tucker and Nancy D. Anderson. Libraries Unlimited, 2004.
Call number: QA41.7. T893
Location: Lee Wee Nam Library
- Using the Mathematics Literature. Edited by Kristine K. Fowler. Marcel Dekker, 2004.
Call number: QA41.7.U85
Location: Lee Wee Nam Library
This book is divided into two parts. The first part consists of three chapters
- Mathematics culture
- Tools and Strategies for finding mathematics information and
- Tools and strategies for searching the research literature
The second part consists of recommended resources for subjects such as ‘Abstract Algebra’, ‘Combinatorics’, ‘Number Theory’, ‘Numerical Analysis’, ‘Real and Complex Analysis’ and etc.
- McGraw Hill Dictionary of mathematics. McGraw Hill, 2003.
Call number: QA5.M147
Location: Lee Wee Nam Library
- Elsevier’s Dictionary of Mathematics: in English, German, French and Russian. Elsevier, 2000.
Call number: QA5.E49
Location: Lee Wee Nam Library
This dictionary consists of 2 sections. The first section is an index of over 11,000 mathematical terms in English and their German, French and Russian equivalents. The second section comprises of indexes of German, French and Russian terms, each being cross-referencd to its English equivalent.
Encyclopedias provide information such as overview to a topic, formulas and facts. Many entries in these works are accompanied by a selective list of references.
- CRC Concise Encyclopedia of Mathematics. Second Edition [e-book via CRCNetBASE]
Call number: QA5.W433
A compendium of mathematical definitions, formulas, figures, tabulations, and references compiled by Eric Weisstein. The material from this encyclopedia has been incorporated intoMathWorld, an internet resource.
- Encyclopedic Dictionary of Mathematics, 4 volumes, 2nd ed. MIT, 1987.
Call number: QA5.I96
Location: Lee Wee Nam Library
This dictionary consists of 450 articles covering areas such as Logic and Foundations; Sets, General Topology, and Categories; Algebra; Group Theory; Number Theory; Algebraic Geometry; Topology; Complex Analysis; Differential, Integral, and Functional Equations; Numerical Analysis; Computer Science and Combinatorics; Probability Theory; Mathematical Programming and Operations Research.
- Encyclopedia of Statistical Sciences 2nd ed. Wiley, 2005 [e-book via Wiley Online]
Handbooks and Tables
These resources provide concise information on practical aspects of mathematics, example, data, formulas, techniques and principles.
- CRC Standard Mathematical Tables and Formulae, 31st Edition. CRC Press, 2003.
Call number: QA47.C911
Location: Lee Wee Nam Library [e-book via CRCNetBASE]
- CRC Standard Probability and Statistics Tables and Formulae. Chapman & Hall / CRC, 2000. [e-book via CRCNetBASE]
- Handbook of Graph Theory. CRC Press, 2004.
Call number: QA166.H236
Location: Lee Wee Nam Library [e-book via CRCNetBASE]
An overview of graph theory presented in 11 chapters. Definitions, facts, examples and a list of references are provided for each topic.
- Handbook of linear algebra. CRC Press, 2007. [e-book via CRCNetBASE].
This handbook covers major topics of linear algebra at undergraduate and graduate levels, and its applications.
- Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables. Edited by Abramowitz, Milton and Irene Stegun. National Bureau of Standards, 1972.
Call number: QA47.H236
Location: Lee Wee Nam Library [e-book via Knovel]
- Table of Integrals, Series, and Products 7th edition. Academic Press, 2007.
Call number: QA55.G733 2007 + 1 CD
Location: Lee Wee Nam Library
This reference work consists primarily of formulas and include results for ‘Indefinite Integrals of Elementary Functions’, ‘Definite Integrals of Special Functions’, ‘Algebraic Inequalities’, ‘Determinants’, ‘Ordinary Differential Equations’, ‘Fourier’, ‘Laplace and Mellin Transforms’ and etc. Errata to this edition and earlier editions are available for reference.
The Library subscribes to many databases, covering many subject areas. In this section, we look at bibliographic databases relevant to Mathematics.
A bibliographic database is an information silo and typically contains the following features:
- An index to bibliographic information (author, title, keywords, abstract and etc) of publications such as journal papers, conference papers, books, and newspapers
- A powerful interface to search this index, and
- Links to full-text articles in the Library e-journal collection
The core bibliographic databases relevant to mathematics are listed below. Use an appropriate bibliographic database to find journal or conference papers on a topic of interest.
When gathering reference materials for a comprehensive literature review, it may be necessary to search multiple databases. You may also need to use computer science, engineering, social sciences, or multidisciplinary databases to locate papers related to the applications of mathematics in those areas.
- Current Index to Statistics
Source: American Statistical Association and the Institute of Mathematical Statistics
Coverage: from 1975 to present
This database contains information for more than 240,000 journal papers and over 50,000 conference papers in statistics, probability, and related fields. View its Database information page.
Source: American Mathematical Society
This database is the electronic version of the ‘Mathematical Reviews’ and covers literature in pure and applied mathematics, statistics and applied statistics, and computer science, among others. It has over over 2 million bibliographic records and about 100,000 new entries added each year. Publications indexed in MathSciNet include journal articles, conference papers, technical reports and book reviews. View its Database information page.
- Zentralblatt MATH
Source: European Mathematical Society (EMS), Fachinformationszentrum (FIZ) Karlsruhe, and the Heidelberger Akademie der Wissenschaften.
This database has over 2.8 million entries and about 85,000 added per annum. It covers extensive areas of pure and applied mathematics from the period of 1868 to present. View itsDatabase information page.
Search Tip: Using the Mathematics Subject Classification (MSC)
The American Mathematical Society assigned all Mathematics into 97 primary classifications (number of classifications as of Aug 2010). There are three levels of hierarchy in the Mathematics Subject classification (MSC):
|Levels of Hierarchy||Examples|
|1st (Primary): 2-digit code||15: Linear and Multilinear Algebra; Matrix theory
60: Probability Theory and Stochastic Processes
|2nd (Secondary): 3-digit code||15A: Basic Linear Algebra
15B: Special Matrices
60H: Stochastic Analysis
60J: Markov Processes
|3rd (Secondary): 5-digit code||15A06: Linear Equations
15A18: Eigenvalues, Singular Values, and Eigenvectors
15B15: Fuzzy Matrices
15B51: Stochastic matrices
60H05: Stochastic Integrals
60H20: Stochastic Integral Equations
60J10: Markov Chains
60J50: Boundary Theory
Source: Institution of Electrical Engineers
Coverage: 1898 to present
This bibliographic database covers subjects such as mathematical physics, applied mathematics and statistics, and computer science. View its Database information page.
Coverage: 1996 to present
This database is an index to major science, engineering and social sciences journals and also conference proceedings. It also provides citation information (example: citation count) to materials indexed by Scopus. View its Database information page.
- Web of Science
Source: Thomson Reuters
Coverage: 1900 to present (for SCI & SSCI)
This database consists of the Science Citation Index (SCI), Social Science Citation Index (SSCI), Arts & Humanities Index (A & HCI) and Conference Proceedings Citation index. It provides citation count (number of times a paper has been cited) of papers indexed by Web of Science, details of citing and cited articles and more. View its Database information page.
An important process in scientific research is to communicate the results of research. Mathematicians report their research work primarily in academic or scholarly journals. Papers submitted to such journals undergoes a review process by other experts in the same field before they are accepted for publication. Some researchers have also taken to posting articles in pre-print servers to allow quick dissemination of their work.
Some publishers of Mathematics journal include:
- Commercial publisher: Elsevier, Springer and Wiley
- Society publisher: American Mathematical Society, European Mathematical Society and London Mathematical Society
- University press: Duke University, Oxford University and Princeton University
The Library has over 100 mathematics journal titles and most of them are accessible electronically.
Search for an e-journal subscribed by the Library
Look at the following journal citation example, and use the E-Journals A-Z List to locate the e-journal.
G. Lawler, O. Schramm, and W. Werner. Conformal restriction: The chordal case. J. Amer. Math. Soc., 16(4):917-955 (electronic), 2003. MR1992830 (2004g:60130)
The journal title is in bold and is abbreviated. Use truncation symbol * to search abbreviated journal titles. For example, instead of “J. Amer. Math. Soc.”, you may use “J* Amer* Math* Soc*”. See below diagram.
Do take note of the coverage that the corresponding different source providers offer.
The back issues of some titles may not available electronically, hence, you may have to refer to the print copies. To check the availability of print journals, you can use the Library Catalogue and search using the ‘journal title’ field if you know the title of the journal.
If you are unable to locate the journal article that you need for your research, you may want to use ourDocument Delivery Service to request for the Library to purchase the article.
Selected journals that publish papers in broad areas of Mathematics
Click on the titles to launch it. You may be prompted for your NTU Network username and password.
- Acta Mathematica (all areas of mathematics)
- Advances in Mathematics (pure mathematics)
- Bulletin of the American Mathematical Society (all areas of contemporary mathematics)
Publisher: American Mathematical Society
- Bulletin of the London Mathematical Society (mainly pure mathematics)
Publisher: London Mathematical Society
- Communications on Pure & Applied Mathematics
- Inventiones Mathematicae (all areas)
- Journal of the American Mathematical Society (all areas pure & applied)
Publisher: American Mathematical Society
- Mathematische Annalen (broad spectrum of modern mathematics)
The Audio Visual Collection is located in the Business Library at level B2. You can find some interesting titles for those who are curious about Mathematics and its applications there.
While staff and postgraduate students can borrow the titles home, undergraduate students can only view the AV materials with the viewing facilities within the library. My picks of DVDs are listed below, including lectures, educational movies and inspiring biographical films. Click on the titles to check their availability in the Library.
- How to make better decisions (50 min.)
[London]: BBC/Discovery Co-production, c2007.
Call number: HD30.23.H847T
Do you know that Mathematics can help people make important decisions? Watch Garth Sundem’s attempts in solving real life dilemmas such as dating, shopping with mathematics.
- Why maths doesn’t add up (52 min.)
Frenchs Forest, N.S.W.: BBC Active/Person Australia, 
Call number: QA11.W629
In this video, we meet Marcus du Sautoy who is not only passionate about mathematics but also loves to share his interest in the subject with the public.
- The joy of thinking: the beauty and power of classical mathematical ideas (4 DVDs, 720 min.)
Arlington, VA: Teaching Co., c2003.
Call number: QA7.B954
Contrary to popular belief that mathematics is a hard science, classical mathematics can be an artistic and creative realm containing some of the greatest ideas of human history which shaped our cultures.
- Archimedes’ secret (50 min.)
Frenchs Forest, N.S.W.: BBC Active, 2006.
Call number: QA31.A673A
This program takes a look at the manuscript copy of Archimedes’ revolutionary mathematical theories.
- Life by the numbers (7 DVDs, 399 min.)
Thousand Oaks, Calif.: Monterey Video: Distributed by Monterey Media, Inc., 2006.
Call number: QA93.L722
Mathematics is related to our everyday life. This video shows us how we can use mathematics to explore our world and make our lives better.
- N is a number: a portrait of Paul Erdös (57 min.)
Berlin: Springer-Verlag, c2005.
Call number: QA29.E68 BN57 2004
The Hungarian mathematician, Paul Erdös, is well known for his “legendarily eccentric” personality. This film presents his quest, as well as the tragic historical events that molded his life.
- A brilliant madness (60 min.)
[Alexandria, Va.]: PBS Home Video; Burbank, CA: Distributed by Warner Home Video, c2002.
Call number: QA29.N25B857
A documentary television program presents the dramatic biography of John Nash, an American mathematical genius who suffers from schizophrena.
- A beautiful mind (135 min.)
Universal City, Calif.: Universal Studios, , c2001.
Call number: PN1995.9.B384 2002
This is a biographical film of John Nash, an American mathematical genius.
- [Pi] (85 min.)
Santa Monica, Calif.: Artisan Entertainment, c1998.
Call number: PN1995.9.M463P579 1998
Want to have an idea how patterns in the stock market can be predicted? Learn about how a brilliant mathematician teeters on the brink of insanity as he conducts his research in this area.
Below is a list of selected web resources on Mathematics.
Content at a Glance
Website – Scholarly Societies
- American Mathematical Society (AMS)
Founded in 1888, AMS offers programs that promote mathematical research, increase the awareness of the value of mathematics to society, and foster excellence in mathematics education.
- ASA – American Statistical Organization
ASA was founded in 1839 to foster excellence in the use and application of statistics.
- Australian Mathematical Society
This site offers information about Mathematics in Australia, including publications, events, careers and etc.
- Canadian Mathematical Society (CAS)
Founded in 1945, CAS focuses on the future and the forming of new partnerships with the users of mathematics in business, governments and universities, educators in the school and college systems as well as other mathematical associations.
- European Mathematical Society (EMS)
EMX was founded in 1990 to further the development of all aspects of Mathematics in the countries of Europe.
- MAA Online
The Mathematical Association of America.
- SIAM Society
Society for Industrial and Applied Mathematics. SIAM provides information on mathematics related books, journals, and conferences.
The open-content textbooks collection includes books in Mathematics.
A Wikimedia Foundation project devoted to learning resources, learning projects, and research for use in all levels, types, and styles of education from pre-school to university, including professional training and informal learning.
- Google Scholar
This site provides a search of scholarly literature across many disciplines and sources, including theses, books, abstracts and articles.
Free online service that provides web resources selected by subject specialists.
Comprehensive science-specific search engine on the internet
Free federated search tool for scholarly literature of various leading science and technology publishers.
Comprehensive virtual library and reference tool for academic and scholarly Internet resources, built by librarians.
- Encyclopaedia of Mathematics, edited by Michiel Hazewinkel
- Eqworld – The world of Mathematical Equations
History of mathematics
Reserves / RBR titles / Red-spot books are recommended textbooks selected by your lecturers for your course modules.
Browsing the Reserves collection
The Reserves collections for Mathematics and Economics are located at the Library Outpost (Learning Hub level 1), with Year 1 & 2 books in the ARM (Automated Reserves Machine) outside the Library Outpost. All Reserve titles are marked for a 2-hour loan each and are easily identified by the red spot on the book spine.
RBR titles can be borrowed at the service desks or the self-check machines located within the Reserves section. Overdue fines for RBR titles are set at $0.50 per hour so be sure to return them on time.
Searching for Reserve titles
You can search RBR titles by their Course Numbers.
- Go to the Library Catalogue and click on the Reserves tab on the top right-hand side
- Key in the course code
- Click Search by Course ID
NTU student’s reports (FYP/IA/PA/PI) and theses are found in our Digital Repository, DR-NTU (Restricted Access). To log in and view the full text, NTU staff or student network username and password will be needed.
Searching for Students’ Works
At the SPMS Student Reports page, you can
- Browse by ‘Titles’, ‘Authors’ or ‘Subjects’ (example: Mathematics:Mathematical logic),
- Search using keywords or
- Search by supervisor’s name.
NTU Staff are encouraged to submit their publications to our institutional repository, Digital Repository, DR-NTU (Open Access).
Journal articles and conference papers written by NTU faculty and archived in the DR-NTU (Open Access) are searchable using Internet search engines such as Google Scholar.
Many publishers allow self archiving of publications in institutional repositories. You may refer to the copyright policies and archiving guidelines from Sherpa Romeo for more information on these publishers.
If you would like to submit your journal article or conference paper for inclusion our collection, please see the instructions about submissions to DR-NTU or contact your subject librarian.
Access Mathematics staff papers.