1. Course Description
Mathematical
Knowledge first developed for practical needs that provided great intellectual
interest to ancient scholars in different civilizations. In course of getting
solutions of practical problems like problem of antiquity they got stuck and later
developed new outlook and love to enhance and enrich knowledge for the sake of
knowledge even with no practical application in mind. But in later period other
areas were discovered where theoretical mathematics were used. Thus this course
deals with a very brief history of mathematics with respective contributions of
mathematicians involved.
2. General Objectives: The general
objectives of this course are to encourage and enable students to
i.
Recognize
that mathematics permeates the world around us.
ii.
Appreciate
the usefulness, power and beauty of mathematics.
iii.
Appreciate
the internal dimension and development of mathematics in relation to its
multicultural and historical perspectives.
iv.
Develop
a critical appreciation to reflect upon the work of different mathematicians
who added some knowledge in existing knowledge.
v.
Describe
the developmental aspects in the growth of different sectors (Arithmetic,
geometry, algebra, trigonometry, calculus and probability) of mathematics.
3. Specific Objectives and Contents
Students are expected to describe
the major concepts of each mathematician who added some bricks in the
development of specific subject area. So, at the end of the course, students
should be able to:
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Contents |
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Unit: I: Historical Development
of Arithmetic (15) 1.1 Ancient Period: Egyptian,
Hindu, Babylonian, and Chinese 1.2 Medieval Period 1.3 Modern Period
|
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Unit: II: Historical
Development of Geometry (24) 2.1 Early Greeks 2.2 Analytic Geometry 2.3 Projective and Descriptive
Geometry 2.4 Algebraic Geometry 2.5 Differential Geometry 2.6 Non-Euclidean Geometry 2.7 Topology |
|
Unit: III: Historical
development of Equations and Algebra (26) 3.1 Equation, Determinant and
Matrix 3.2 Equation, group, and field 3.3 Link with Analysis 3.4 Link with Number theory 3.5 Link with Linear Algebra |
|
Unit: IV: Historical
development of Trigonometry (14) 4.1 Ancient Period 4.2 Medieval period 4.3 Trigonometric function 4.4 Trigonometric series |
|
Unit: V: Historical development
of Calculus and Analysis (26) 5.1 Exposition of calculus 5.2 Differential Equation 5.3 Calculus of variation 5.4 Analysis
|
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Unit: VI: Historical
development of Functions (13) 6.1 Ancient Period 6.2 Medieval Period 6.3 Modern Period |
|
Unit: VII: Historical
development of Statistics and Probability (21) 7.1 Laws of large number 7.2 Central Limit Theorem 7.3 Statistics 7.4 Large number and limit
theorems
|
|
Unit VIII Development of
Mathematics in Nepal (11) 8.1 Ancient Period 8.2 Medieval Period 8.3 Modern Period |
1. Instructional Techniques
|
Unit |
Specific
instructional Techniques |
|
I |
Lecture methods, Question-answer
methods on different civilizations: Ancient Period: Egyptian, Hindu,
Babylonian, and Chinese. Medieval Period: Aryabhat, Mahavira, Modern Period:
Peano, Weierstrass Poincare |
|
II |
Presentation followed feedback
session on the contribution of Pythagoras, Euclid, Proclus, Descartes,
Fermat, Newton, Gauss, Lobachevsky, Riemann, Monge, Steiner, and Hilbert |
|
III |
Project given in a group on the
contribution of Diophantus, Hypatia, Brahmagupt, Bhaskara, Al-Khwarismi, Fibonacci, Viete,
Descartes, Fermat, Agnesi (cubic curve), Gauss, Euler, Galois, Boole,
Hamilton, Noether |
|
IV |
Lecture methods followed by
discussion on the contribution of Thales, Eratosthenes, Ptolemy, Aryabhatta, Regimontanus, Viete, Euler |
|
V |
Presentation followed feed back
session on the contribution of Zeno, Eudoxus, Archimedes, Pappus, Kepler,
Cavaliers, Leibnitz, Newton, Bernoulli, L’Hospital, Euler, Laplace, Cauchy,
Weirestrass, Dedekind, Riemann, Sonja, Labesque |
|
VI |
Lecture methods followed by
discussion on the contribution of Ancient Period, Medieval Period, Leibnitz,
Euler, Fourier, , Dirchlet, Cantor |
|
VII |
Presentation on the
contribution of Pascal, Fermat, Huygens, Cardano, Bernoulli. De Moivre,
Lagrange, Laplace, Gauss, Poisson, Chebyshevs, Galton, Pearson, Fisher,
Newman |
|
VIII |
Guest lecture on the
contribution of Gopal Pande, Naya Raj Panta,
Chakra Pani Aryal, Chandra Kala Devi Dhananjaya |
|
Suggestion |
Most of topics are covered from
the book written by Cooke. Further elaboration supposed to covered by other
books. |
2. Evaluation
|
Type of questions |
Total question asked |
Marks allotted |
Total Marks |
|
Group A: Multiple choice |
20 questions |
20 x 1 marks |
20 Marks |
|
Group B: Short Answer |
8 with 3 alternative |
8 x 7 marks |
56 marks |
|
Group C: Long Answers |
2 with 1 alternative |
2 x 12 marks |
24 marks |
3. Recommended Books and Reference
Books
Cooke, R. (1997). The history of mathematics: A brief course.
New York: John Wiley & Sons, Inc. (Unit
I-VII)
Eves, H. (1984). An introduction to the history of
mathematics (5th ed.). New York: The Saunders series.
Pant, N. R. (1980). Gopal Pande & his rule of cube root.
Kathmandu: Nepal Academy
Bhattarai, L. N,;
Adhikari, K. P. & Neupane, A. (2013). The
history of mathematics, (1st ed.). Kathmandu: Quest Publication
Pvt. Ltd.
Bhushan, B. D. et. al
(2011). History of Hindu Mathematics
(part I & II), Cosmo Publications.
Boyer, C. B. (1968). A History of mathematics. New York: John
Willy & Sons Inc.
(Unit I-VII)
Burton, (2007). The History of
Mathematics: An Introduction, (6th ed.), the McGraw−Hill Companies. (Unit
I-VII)
Pant, N. R (1982). Comparison of ancient and new mathematics.
Kathmandu: Nepal Academy
Struik, D. J. (1948). A concise history of mathematics, Vol. I
and II (4th ed.). New York: Dover Publication, Inc. (Unit I – VII)
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