Teaching Undergraduate Mathematics

by Burn, R. P.; Appleby, John; Maher, Philip

• ISBN13: 9781860941153
• ISBN10: 186094115X
• Format: Hardcover
• Copyright: 1998-06-01
• Publisher: Imperial College Pr

Table of Contents

Foreword	v
Sir Michael Atiyah
Introduction	1	(1)
List of Themes	2	(2)
Acknowledgements	4	(1)
Glossary of UK Educational Terms	4	(1)
1. The Undergraduate Mathematics Teaching Conferences--the Source of the Material	5	(4)
2. The Process of Teaching Mathematics	9	(78)
2.1 The New Student	9	(2)
2.2 The New Lecturer	11	(5)
2.3 Teaching Undergraduates	16	(21)
2.3.1 Some Inbuilt Problems	16	(1)
2.3.2 Modes of Teaching	16	(5)
2.3.3 Good Practice	21	(1)
2.3.3.1 Effective Lecturing	21	(1)
2.3.3.2 Tutorials	22	(6)
2.3.3.3 Self-paced Learning	28	(4)
2.3.3.4 Projects	32	(5)
2.4 Communication	37	(32)
2.4.1 Communicating What?	37	(9)
2.4.2 Books	46	(8)
2.4.3 Microcomputers	54	(14)
2.4.4 Video	68	(1)
2.5 Appraisal	69	(11)
2.6 The Future	80	(7)
3. Content of A-level and Undergraduate Mathematics	87	(36)
3.1 Rigour at A-level	87	(15)
3.2 First Year Undergraduate Courses	102	(9)
3.3 Geometry	111	(12)
4. Detailed Expositions	123	(18)
4.1 Analysis	123	(13)
4.2 Number Theory	136	(1)
4.3 Quadratic Equations	137	(1)
4.4 Friction	138	(3)
5. History of Mathematics	141	(20)
5.1 History of Mathematics in the Undergraduate Curriculum	141	(10)
5.1.1 Why History of Mathematics?	142	(1)
5.1.2 Construction of Courses in the History of Mathematics	143	(3)
5.1.3 The Cameo Approach	146	(2)
5.1.4 Bibliography and Other Materials	148	(3)
5.2 Education Imitating History	151	(10)
6. Needs of Society and the Professions	161	(26)
6.1 Mathematics for the Needs of Society	161	(8)
6.1.1 Adapting the Undergraduate Curriculum	161	(3)
6.1.2 Courses on `Mathematics in Society'	164	(5)
6.2 Mathematics for Employment	169	(8)
6.3 Mathematics for the Teaching Profession	177	(4)
6.3.1 University Mathematics and the Teaching of Mathematics in Secondary Schools	177	(2)
6.3.2 Routes into the Teaching Profession	179	(2)
6.4 Service Teaching of Mathematics	181	(6)
6.4.1 Traditional	181	(1)
6.4.2 Service Teaching to Biologists	182	(3)
6.4.3 Mathematics for Computer Science	185	(1)
6.4.4 Service Teaching for Liberal Arts	186	(1)
7. Applications and Modelling	187	(36)
7.1 Applications of Mathematics	187	(9)
7.2 Why isn't Modelling Taught More Widely?	196	(3)
7.3 Classical Applications vs Modelling	199	(4)
7.4 The Experience of Mathematical Modelling	203	(20)
8. Learning Mathematics	223	(24)
8.1 Enjoyment	223	(3)
8.2 Learning (or not learning) Mathematical Concepts	226	(7)
8.3 Self-assessment and Peer Support	233	(1)
8.4 Intuition and Experiment	234	(2)
8.5 What Balance of Learning Activities do Students Need?	236	(11)
9. Assessment	247	(18)
9.1 Assessment by Lecturers	247	(12)
9.2 Peer Assessment	259	(6)
Index	265