數學學系: 課程參考資料

課程名稱/教師

課程參考書目

微分方程導論/微分方程特論
陳賢修/林惠娥/林月珍

Boyce, W. E. & DiPrima, R. C. (2001). Elementary differential equations and boundary value problems. New York : Wiley.

代數學（一）/代數學探索（一）

劉家新

Herstein, I. N. (1996). Abstract algebra. Upper Saddle River, N.J. : Prentice-Hall.

離散數學
郭君逸 

Tucker, A. (2007). Applied combinatorics. Hoboken, N.J. : John Wiley.
Brualdi, R. A.(2012).  Introductory Combinatorics(5th  ed.). Upper Saddle River, N.J. : Pearson Prentice Hall.
Dossey, J. A.… et al.(2006). Discrete mathematics. Boston : Pearson Addison-Wesley. (圖形學)

高等幾何（一）

左台益

Anderson, J. W. (2005). Hyperbolic Geometry [electronic resource]. London : Springer-Verlag London Limited.
Cederberg, J. N. (2001). A course in modern geometries. New York : Springer.
Eves,H. (1992). Fundamentals of modern elementary geometry. Jones and Bartlett Publishers, Inc.
Libeskind, S. (2008). Euclidean and transformational geometry. Jones and Bartlett Publishers, Inc. 9780763743666
Meyer, W. J. (1999). Geometry and its applications. San Diego : Academic Press. (有電子書)
Hilbert, D. & Cohn-Vóssen, S. (1952). Geometry and the imagination. New York : Chelsea Pub. Co.

微分方程導論
陳賢修/林月珍/林惠娥

Ross, S. L. Differential equations. New York, Blaisdell Pub. Co.

高等微積分（一）/
高等微積分探索（一）
謝世鋒/林延輯/蔡志強

Rudin, W. (1976). Principles of mathematical analysis. New York : McGraw-Hill.
Apostol, T. M. (1974). Mathematical analysis. Reading, Mass. : Addison-Wesley Pub. Co.
Fitzpatrick.  Advanced Calculus, a course in mathematical analysis.
Protter, M. H. & Morrey, C. B. (1991). A first course in real analysis. New York : Springer-Verlag.
Wade, W. R. (2004). An introduction to analysis. Upper Saddle River, NJ : Pearson Education.
趙文敏（2000-2005）。高等微積分。臺北市：五南。

代數學（一）/
代數學探索（一）

劉家新/紀文鎮/洪有情

Gallian, Contemporary abstract algebra.
Lanski, C. (2005). Concepts in abstract algebra. Australia : Thomson. Brooks-Cole. (9780534423230)

Herstein. Abstract Algebra
Fraleigh, J. B. (1999). A first course in abstract algebra. Reading, Mass. : Addison-Wesley.

課程名稱/教師

課程參考書目

數值分析（一）
黃聰明 

Burden, R. L. & Faires, J. D. (1993). Numerical analysis. Boston : PWS-Kent Pub. Co.
Kincaid, D. & Cheney, E. W. (1991). Numerical analysis : mathematics of scientific computing. Pacific Grove, Calif. : Brooks/Cole. 

高等線性代數（一）

李華介/劉容真

Friedberg, S. H., Insel, A. J., & Spence, L. E. (1989). Linear algebra. Englewood Cliffs, N.J. : Prentice Hall.

Curtis, C. W. (1997). Linear algebra : an introductory approach. New York : Springer-Verlag.

Blyth, T. S. & Robertson, E. F. (2002). Further linear algebra. London ; New York : Springer.http://link.springer.com/book/10.1007/978-1-4471-0661-6 
Hungerford, Algebra (chapter VII) (GTM) 

Hoffman, K.& Kunze, R. Linear Algebra.

複變數函數論
張毓麟/陳瑞堂 

龔昇（1997）。複變函數論。臺北市：新陸。(9789579147026)
Brown, J. W. & Churchill, R. V. (2009). Complex variables and applications. Boston : McGraw-Hill Higher Education.
Marsden, J. E. & Hoffman, M. J. (1973). Basic complex analysis. San Francisco : W. H. Freeman.

Ahlfors, L.V. (1979), Complex Analysis, 3rd ed., McGraw-Hill.

Bak, J., Newman D.J. (1997), Complex Analysis, 2nd ed., Springer-Verlag.

微分幾何（一）

林俊吉/陳瑞堂 

Shifrin, T., (2016).Differential Geometry: A First Course in Curves and Surfaces.

Manfredo P. Do Carmo, Differential Geometry of Curve and Surfaces

Gray, A. (1998). Modern differential geometry of curves and surfaces with Mathematica. Boca Raton : CRC Press.
O'Neill, B. (2006). Elementary Differential Geometry. Burlington : Elsevier.

代數特論（一）
劉容珍

Fraleigh, J. B. (1999). A first course in abstract algebra. Reading, Mass. : Addison-Wesley.

高等微積分特論
張幼賢 

Apostol, T. M., Mathematical Analysis, Addison-Wesley.  Bachman, G. et al., Fourier and Wavelet Analysis, Springer-Verlag.

Protter, M. H. & Morrey, C. B. (1991). A first course in real analysis. New York : Springer-Verlag.

Rudin, W., Principles of Mathematical Analysis, McGraw-Hill.

Wheeden, R., Zygmund, A., Measure and Integral: an Introduction to Real Analysis, Dekker.

趙文敏, 高等微積分, 〈上〉、〈下〉冊, 五南出版社.

統計學（一）
張少同/呂翠珊/蔡碧紋

Ross, S. (2014) A First Course in Probability, Prentice Hall, 9th edition.

Hogg, R. V. & Tanis, E. A. (2015). Probability and Statistical Inference(9th ed). Prentice Hall. 
Rice, John A. (1995). Mathematical Statistics and Data Analysis(2nd ed.). Duxbury Press. (9780534399429, 3rd ed.)

課程名稱/教師

課程參考書目

數學史
洪萬生 

柏林霍夫、辜維亞（2008）。溫柔數學史：從古埃及到超級電腦（洪萬生、英家銘暨HPM團隊譯）。臺北市：博雅書屋。
內茲、諾爾（2007）。阿基米德寶典：失落的羊皮書（曹亮吉譯）。臺北市：天下遠見出版：大和書報總經銷。
克萊（2004）。數學：確定性的失落（趙學信、翁秉仁譯）。臺北市：臺灣商務。
李文林（2000）。數學珍寶：歷史文獻精選。臺北市：九章出版；臺北縣中和市：成信文化總經銷。
李儼、杜石然（1983）。中國古代數學簡史。臺北市：九章出版；臺北縣新店市：學英文化總經銷。
洪萬生（1993）。談天三友。臺北市：明文。
洪萬生（1999）。孔子與數學：一個人文的懷想。臺北市：明文。
洪萬生（1999）。從李約瑟出發：數學史、科學史文集。臺北市：九章出版；臺北縣新店市：成信文化總經銷。
洪萬生（2006）。此零非彼0：數學、文化、歷史與教育文集。臺北市：臺灣商務。
洪萬生（2006）。數之起源：中國數學史開章<>。臺北市：臺灣商務。
郭書春（1994）。中國古代數學。臺北市：臺灣商務。
郭書春（1995）。古代世界數學泰斗劉徽。臺北市：明文。
郭書春（1990）。九章算術。瀋陽市：遼寧教育出版社出版：遼寧省新華書店發行。
郭書春（2004）。匯校九章筭術。瀋陽市：遼寧教育出版社。(有電子書)
郭書春、劉鈍主編（1998）。李儼、錢寶琮科學史全集。瀋陽：遼寧教育出版社。(9787538248074)
郭書春、劉鈍（2001）。算經十書。臺北市：九章出版；[臺北縣中和市]：成信總經銷。
刘钝（1993）。大哉言数。瀋陽市：遼寧教育出版社出版：遼寧省新華書店發行。
克蘭（1996）。高觀點下的初等數學（舒湘芹、陳義章、楊欽樑譯）。臺北市：九章出版；臺北縣新店市：學英總經銷。
歐森林（2001）。女數學家列傳（彭婉如、洪萬生譯）。臺北市：九章。
Berlinghoff, W. P. & Gouvea, F. Q. (2004). Math through the ages : a gentle history for teachers and others. Farmington, ME : Oxton House Publishers ; Washington, DC : Mathematical Association of America.
Bunt, L. N. H., Jones, P. S., & Bedient, J. D. (1988). The historical roots of elementary mathematics. New York : Dover Publications.
Courant, Richard, & Herbert Robbins (revised by Ian Stewart) (1996). What is Mathematics? New York ; Oxford: Oxford University Press.（大一「數學導論」教學用書） 9780195105193
Dunham, W. (1990). Journey through genius : the great theorems of mathematics. New York : Wiley.
Grattan-Guinness, I. (1997). The Fontana history of the mathematical sciences : the rainbow of mathematics. London : Fontana Press.
Katz, V. J. (2008). A history of mathematics : an introduction. Boston : Pearson Addison-Wesley.
Struik, D. J. (1987). A concise history of mathematics. New York : Dover Publications.

數學教學實習（一）（教）
林福來/楊凱琳

謝豐瑞/王婷瑩 

國家教育研究院籌備處（2007-）。國民中學數學課本。[臺南市]：國家教育研究院籌備處出版：翰林發行。
台灣省中等學校教師研習會、教育部國民教育司（1992）。國民中學教學方法手冊。臺北市：教育部國民教育司。
教育部國民教育司（1991）。國民中學教學評量手冊。臺北市：教育部國民教育司。
台灣省中等學校教師研習會、教育部國民教育司（1992）。國民中學教學媒體手冊。臺北市：教育部國教司。
國立臺灣師範大學實習輔導處（1996）。中等學校各科教案編寫示例。臺北市：臺灣師大輔導處。

高中數學課本及教師手冊，國立編譯館。

中等學校輔導手冊，國立台灣師範大學實習會。

近世代數（一） [大碩合開]
紀文鎮

     Hungerford, T. W. (1996). Algebra. New York : Springer.

Lang, S.(1993). Algebra  3rd edition

實變分析（一） [大碩合開]
朱亮儒 

Wheeden, R. L. & Zygmund, A. (1977). Measure and integral : an introduction to real analysis. New York : M. Dekker.
Aliprantis, C. D. & Burkinshaw, O. (1990). Principles of real analysis. Boston : Harcourt Brace Jovanovich.

複變分析（一） [大碩合開]
張毓麟 

Wunsch, A. D. (1994). Complex variables with applications. Reading, Mass. : Addison-Wesley Pub. Co.
Conway, J. B. (1995). Functions of one complex variable II. New York : Springer-Verlag.

Ahlfors, L. V. (1979). Complex analysis : an introduction to the theory of analytic functions of one complex variable. New York : McGraw-Hill.
Bak, J. & Newman, D. J. (2010). Complex analysis[electronic resource]. New York : Springer Science+Business Media.
Lang, S. (1985). Complex analysis. New York : Springer-Verlag.
Berenstein, C. A. & Gay, R. (1991). Complex variables : an introduction. New York : Springer-Verlag.

迴歸分析 [大碩合開]
張少同

 Chatterjee, Simonoff(2013).andbook of Regression Analysis (Using R), Wiley

Sheather, S. (2009). A modern approach to regression with R [electronic resource]. New York, NY : Springer-Verlag New York. Kutner, Nachtsheim, Neter, Li(2005)Applied Linear Statistical Models 5th ed, McGraw Hill

統計計算 (一) [大碩合開]
蔡碧紋

Ross, M Sheldon Simulation
Rizzo, M. L. (2007) Statistical computing with R. Chapman & Hall/CRC. http://personal.bgsu.edu/~mrizzo/M758/M758.htm

Jones, O., Maillardet, R. and Robinson, A. (2009),  Introduction to Scientific Programming and Simulation Using R,  Chapman and Hall/CRC.   http://www.ms.unimelb.edu.au/spuRs/

Robert, C. P., Casella, G. Monte Carlo Statistical Methods.

The Elements of Statistical Learning: Data Mining, Inference, and Prediction by Trevor Hastie, Robert Tibshirani, Jerome Friedman
James, G., Witten, D., Hastie, T., Tibshirani, R. An Introduction to Statistical Learning With Application in R

編碼學 [大碩合開]
李華介

N. L. Biggs, Codes: An Introduction to Information Communication and Cryptography, Springer, 2008. http://link.springer.com/book/10.1007/978-1-84800-273-9

課程名稱/教師

課程參考書目

數學教育研究法（一）
楊凱琳 [碩博合開]

王文科、王智弘 (2012)。教育研究法。台灣五南圖書出版股份有限公司。(9789571164632)

數學教育通論（一）

曹博盛 [碩博合開]

林清山(民65)。科學教育的心理學基礎(上)。科學教育月刊，1，27-36。
林清山(民65)。科學教育的心理學基礎(下)。科學教育月刊，2，15-20。
林清山(民66)。數學課程設計和數學教學的理論基礎(上)。科學教育月刊，11，10-20。
林清山(民66)。數學課程設計和數學教學的理論基礎(下)。科學教育月刊，12，4-10。
Schoenfeld, A. H. (原著，黃敏晃翻譯) (民76). 解題技能的教學。數學傳播，11(4)，2-20。
Bishop, A. J. (原著，呂玉琴翻譯) (民80)。數學教育中有關社會維度的研究。科學教育月刊，144，20-35。
江金城(民81)。建構主義—兼談數學教育。科學月刊，23(10)，781-786。
Bell, A. (1993). Some experiments in diagnostic teaching. Educational Studies in Mathematics, 24, 115-137.
Boero, P., Gartui, R., Lemut, E., & Mariotti, M. A. (1996). Challenging the traditional school approach to theorems: A hypothesis about the cognitive unity of theorems. Papers presented in the 20th Annual Meeting of the International Group for the Psychology of Mathematics Education.
Clark, L. H., & Starr, I. S. (1996). Secondary and middle school teaching methods (7th ed.). New York: MacMillan.
Cobb, P. (1996). Accounting for mathematical learning in the social context of the classroom. Lecture presented in International Conference of Mathematics Education (edited by Asina, C., Alvareq, J. M., Hodgson, B., Laborde, C., & Pèrezi, A.)
Cooney, T. J., Davis, E. J., & Henderson, K. B. (1975). Dynamics of teaching secondary school mathematics. Atlanta, GA: Houghton Mifflin.
Ernest, P. (1996). Social constructivism as a philosophy of mathematics. Lecture presented in International Conference of Mathematics Education (edited by Asina, C., Alvareq, J. M., Hodgson, B., Laborde, C., & Pèrezi, A.)
Fischbein, E., Jehiam, R., & Cohen, D. (1995). The concept of irrational numbers in high-school students and prospective teachers. Educational Studies in Mathematics, 29, 29-44.
Hart, K. M. (1981). Hierachies in mathematics education. Educational Studies in Mathematics, 12(2), 205-218.
Henderson, K. B. (1967). A model for teaching mathematical concepts. Mathematics Teacher, 60, 573-577.
Joyce, B., Weil, M., & Calhoun, E. (2004). Models of teaching (7th ed.). Boston, MA: Allyn & Bacon. (目前師大圖書館有第六版)
Lee, L., & Wheeler, D. (1989). The arithmetic connection. Educational Studies in Mathematics, 20, 41-54.
McLeod, D. B. (1985). Affective issues in research on teaching mathematical problem solving. In E. A. Silver (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 267-279). Hillsdale, NJ: Lawrence Erlbaum Associates.
National Council of Teachers of Mathematics (1991). Professional standards for teaching mathematics. Reston, VA: .NCTM
NCTM (1995). Assessment standards for school mathematics. Reston, VA: NCTM.
NCTM (2000). Principle and standards for school mathematics. Reston, VA: NCTM.
Piaget, J. (1975). Comments on mathematical education. Contemporary Education, 47(1), 5-10.
Schimitau, J. (1993). Connecting mathematical knowledge: A dialectical perspective. Journal of Mathematical Behavior, 12(2), 179-201.
Schoenfeld, A. H., Gamoran, M., Kessel, C., Leonard, M., Or-Bach, R., & Arcavi, A. (1992). Toward a comprehansive model of human tutoring in complex subject matter domains. Journal of Mathematical Behavior, 11, 293-319.
Sowder, L. (1980). Concept and principle learning. In R. J. Shumway (Ed.), Research in mathematics education (pp. 244-285). Reston, VA: NCTM.
Steinbring, H. (2005). Analyzing mathematical teaching-learning situations—The interplay of communicational and epistemological constraints. Educational Studies in Mathematics, 59, 313-324.
Wiggins, G. (1988). Rational numbers. American Educator, 12(4), 20-25, 45-48.

數理統計（一）

程毅豪

Hogg, R. V., McKean, J. W., & Craig, A. T. (2005). Introduction to mathematical statistics(6th ed). Upper Saddle River, N.J. : Pearson Education. (9780130085078)
Hogg, R. V. & Tanis, E. A. (2006). Probability and statistical inference. Upper Saddle River, N.J. : Pearson Education International ; London : Pearson Education.
Casella, G. & Berger, R. L. (2002). Statistical inference. Pacific Grove, CA : Duxbury Thomson Learning.

Sheldon Ross, A First Course in Probability. 8^th edition.

Rohatgi(1976), An Introduction to Probability Theory and Mathematical Statistics, John Wiley & Sons.

組合學（一）
游森棚 [碩博合開]

Kane: Reflection groups and Invariant Theory

數學課程發展研究專題(一)

左台益 [碩博合開]

Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge: Cambridge University Press.

National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. VA: Author.

偏微分方程式論

林俊吉 [碩博合開]

H. Brezis, Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011.

試題反應理論
蔡蓉青 [碩博合開]

Baker , F. B. (2001). The Basics of Item Response Theory. ERIC Clearinghouse on Assessment and Evaluation.
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response theory. Newbury Park, Calif. : Sage Publications.
Embretson, S. E. & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, N.J. : L. Erlbaum Associates.

互補問題專題
陳界山 [碩博合開]

Complementarity Problems, by George Isac, Lecture Notes in Mathematics, Vol. 1528, Springer-Verlag, 1992.
The Linear Complementarity Problem, by R. W. Cottle, J-S Pang, and R. E. Stone, SIAM, 2009.

數學心理學專題（一）
林福來 [碩博合開]

禮記 學記篇  

Bloom, B. S. (1956). Taxonomy of educational objectives: The classification of educational goals. NY: Longmans.

Bruner, J. S. (1960). On learning mathematics. The Mathematics Teacher, 53, 68-70.

Cuoco, A. A. & Crucio, F. R. (2001). The roles of representation in school mathematics: 2001 Yearbook. Reston: NCTM.

Davis, R. (1984). Learning mathematics: The cognitive science approach to mathematics education. Beckenham: Croom Helm.

Fan, L & Cai J. (2004). How Chinese learn mathematics: Perspectives from insiders. Singapore: World Scientific Publishing.

Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht: D. Reidel.

Lave, J. & Wenger, E. (1991). Situated learning: Legitimate peripheral participation. NY: Cambridge University Press.

Leont’ev, A. N. (1978). Activity, consciousness and personality. NJ: Prentice Hall.

McLeod, D. B. (1992). Research on affect in mathematics education: A reconceptualization. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the national Council of Teachers of Mathematics, pp.575-596, Reston: NCTM.

Piaget, J. (1952). The child’s conception of number. NY: Routledge.

Piaget, J. & Inhelder, B. (1956). The child’s conception of space. London: Routledge & K. Paul.

Piaget, J. & Inhelder, B. (1958). The growth of logical thinking: from childhood to adolescence. France: Basic Books.

Skemp, R. (1979). Intelligence, learning, and action: A foundation for theory and practice in Education. Chichester.

Vygotsky, L. (1986). Thought and Language. Mass.: MIT Press.

李代數

劉家新 [碩博合開]

Introduction to Lie Algebras and Representation Theory by James E. Humphreys.
Lie Algebras of Finite and Affine Type by Roger Carter.

貝氏統計初探
蔡蓉青 [碩博合開]

Gelman, A., Carlin, J.B., Stern, H.S., & Rubin, D.B. (2013). Bayesian Data Analysis. 3rd edition. Chapman & Hall/CRC.
Gill, J. (2008). Bayesian Methods: A Social and Behavioral Sciences Approach.2nd edition. Chapman & Hall/CRC.
Lee, P. M. (2004). Bayesian Statistics: An Introduction. 3rd edition. A Hodder Arnold Publication.
Carlin, B. P. and Louis, T. A. (2000). Bayes and Empirical Bayes Methods for Data Analysis. 2nd edition. Chapman & Hall/CRC.

解析數論(一)

許志農 [碩博合開]

T. Ono, An Introduction to Algebraic Number Theory

S. Lang, An Introduction to Analytic Number Theory I & II

課程名稱/教師

課程參考書目

數學師資培育課程設計(一)

謝豐瑞

Howson, G., Keitel, C., & Kilpatrick, J. (1981). Curriculum development in mathematics. Cambridge: Cambridge University Press.
National Council of Teachers of Mathematics (NCTM) (2000). Principles and standards for school mathematics. VA: Author.