Graphics Reference
In-Depth Information
Niven, I., 1961,
Numbers
:
rational and irrational
, Mathematical Association of America.
A superb introduction for the sixth-former.
Northrop, E. P., 1960,
Riddles in Mathematics
:
A Topic of Paradoxes
, Pelican. (1st UK
edition, 1945, English Universities Press).
Excellent high-school material. Fascinating on series.
O'Brien, K. E., 1966,
Sequences
, Houghton-MiWin.
For beginners.
Po´ lya, G., 1954,
Induction and Analogy in Mathematics
(
Mathematics and Plausible
Reasoning
, vol. 1), Princeton University Press.
Rich with insight into how mathematics works. Gives historical illumination.
Po´ lya, G. and Szego¨ , G., 1976,
Problems and Theorems in Analysis
, vol. 1, Springer.
Hard problems with solutions: a very rich diet.
Quadling, D. A., 1955,
Mathematical Analysis
, Oxford University Press.
Reade, J. B., 1986,
An Introduction to Mathematical Analysis
, Oxford University Press.
As readable as a conventional text can be.
Rosenbaum, L. J., 1966,
Induction in Mathematics
, Houghton-MiWin.
Good sixth-form material.
Rudin, W., 1953,
Principles of Mathematical Analysis
, McGraw-Hill.
Concise and purposeful. A good second course.
Scott, D. B. and Tims, S. R., 1966,
Mathematical Analysis
, Cambridge University Press.
Smith, W. K., 1964,
Limits and Continuity
, Macmillan.
A concrete development of the neighbourhood definition of limit.
Sominskii, I. S., 1961,
The Method of Mathematical Induction
, Pergamon Press (contained
in
Popular Lectures in Mathematics
, vols 1
—
6 trans. H. Moss).
Excellent sixth-form material for the student willing to do some work!
Spivak, M., 1967,
Calculus
, Benjamin.
The modern lecturer's favourite text: beautifully written, copiously illustrated, and
with an extensive collection of exercises.
Stewart, I. and Tall, D., 1977,
he Foundations of Mathematics
, Oxford University Press.
A serious introduction to university mathematics.
Swann, H. and Johnson, J., 1977,
Prof
.
E
.
McSquared
'
s Original
,
Fantastic and Highly
Edifying Calculus Primer
, William Kaufmann.
A comic-strip approach to functions and limits (by neighbourhoods).
Tall, D., 1982, The blancmange function: Continuous everywhere but differentiable
nowhere.
Math
.
Gaz
., 66,11
—
22.
Tall, D., 1992, The transition to advanced mathematical thinking: functions, limits, infinity
and proof. Articlein Grouws, D. A. (ed.),
Handbook of Research on Mathematics
Teaching and Learning
, Macmillan.
A useful survey of recent research.
Thurston, H. A., 1967,
The Number
-
system
, Dover.
A useful combination of logic and rationale in the development of the number system.
Toeplitz, O., 1963,
The Calculus
:
A Genetic Approach
, University of Chicago Press.
History: thekey to a humaneapproach to analysis.
Wheeler, D., 1974,
R
is for Real
, Open University Press.
A problem-motivated introduction to the real numbers.
Yarnelle, J. E., 1964,
An Introduction to Transfinite Mathematics
, D. C. Heath.
Themost readableaccount of countability that I know.
Zippin, L., 1962,
Uses of Infinity
, Mathematical Association of America.
T