 
On the shelf of any professional software
engineer should be some number of math books. Without these books, the
profession of software developed is reduced to "writing programs." In
principle this is not a problem, until it becomes one. A problem of performance
analysis, reliability calculation, and general mathematical modeling of systems.
Many of these texts I have used in my practice. Others have been used in the
class room.
Probability and Statistics
 Probability and Statistics,
Blum and Rosenblatt, 1972. This is an all encompassing text, with calculus
based statistics and probability.
 Introduction to Probability and Statistics
with Reliability, Queuing, and Other Computer Science Applications,
Kishor Trivedi, Prentice Hall, 1982. This is the classic computer science
math book.
 Introduction to Probability Models 7th
Edition, Sheldon Ross, Academic Press. The text is suited for those
wanting to apply probability theory to the study of phenomena in fields such
as engineering, management science, the physical and social sciences, and
operations research.
 Advanced Theory of Statistics: Vol
1 Distribution Theory, Kendell and Stuart,
McMillan, 1977 is part of a three volume series, which consists of Advanced
Theory of Statistics : Bayesian Inference, Vol 2B, Advanced Theory of
Statistics : Classical Inference and the Linear Model, Advanced Theory
of Statistics : Design and Analysis, and TimeSeries.
Calculus
 The classic book on calculus is Thomas. I
had one in college, but have since lost it. Good used book stores have them
from 5 times the original price.
Queuing
Theory
 Queuing Systems Volume 1: Theory and
Volume 2: Computer Applications, Leonard Kleinrock, Academic Press. This
are the classic queuing theory books. If you don't own this set, you should
have at least heard of them.
 Simulating Computer Systems: techniques
and Tools, M. H. MacDougall, MIT Press. This is a useful book with
software included that describes the theory and practice of simulating
computer systems.
 Queues, D. R Cox and Walter L. Smith,
Chapman and Hall. This is a foundation book describing the theory of queues
and their application.
 Renewal Theory, D. R. Cox, Methuen's
Monographs. This is another foundation book that should be on the
shelf.
 The Practical Performance Analyst,
Neil J. Gunther, McGraw Hill. This book is not really about queues, but is a
replacement for queuing theory books used for performance analysis. In this
book, systems are assumed to be in macroscopic metastable states. With this
assumption much of the non–closed form queuing theory problems are removed
and a much simpler approach is provided to solving common problems
Systems Modeling
Reliability
Performance Analysis
General
Engineering Math
Differential Equations (both ordinary
and partial DEQ's)
Linear Programming
