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Theory
There are a number of theoretical and applied mathematical issues that
are central to laboratory research. These encompass a wide array of
problems from cellular biophysics, chemical network analysis, fundamental
control theory, stochastic process and dynamical systems theory, machine
learning and statistics.
The goals of the theory in this group is to facilitate the analysis
of complex biological systems at multiple levels of abstraction and
in sufficient detail and accuracy to allow control or engineering of
these systems or to elucidate fundamental principles of their operation.
For a description of a few research topics in the lab see the Theory
research page.
People interested in this type of research might benefit from reading
various of the following literature references:
For physically minded people:
Biology
These first few are very short summaries of the field and may be a
little out of date. But each is only a night's reading. For more advanced
biology texts see the Experiments pages.
| Title |
Authors |
Link |
| DNA Structure and Recognition (In Focus Series) |
STEPHEN NEIDLE |
[oxford] |
| DNA Replication (In Focus Series) |
ROGER L. P. ADAMS |
[oxford] |
| Gene Structure and Transcription (In Focus Series)
|
Trevor Beebee, J. Burke |
[amazon] |
| Protein Biosynthesis (In Focus Series) |
H. R. V. ARNSTEIN and R. A. COX |
[oxford] |
| Protein Structure (In Focus Series) |
N. J. DARBY and T. E. CREIGHTON, |
[oxford] |
| Understanding the Control of Metabolism (Frontiers
in Metabolism Ser. ; No. 2)) |
David Fell |
[amazon] |
| The Machinery of Life |
David S. Goodsell |
[amazon] |
| A Genetic Switch : Phage and Higher Organisms |
Mark Ptashne |
[amazon] |
Mathematical Biology
| Title |
Authors |
Link |
| Mathematical Biology (Biomathematics, Vol 19) |
J. D. Murray, S. A. Levin (Editor) |
[amazon]
|
| Mathematical Models in Biology (Random House/Birkhauser
Mathematics Series) |
Leah Edelstein-Keshet |
[amazon] |
Numerical Methods
| Title |
Authors |
Link |
| Numerical Recipes in C |
William H. Press, Saul A. Teukolsky, William T. Vetterling, Brian
P. Flannery |
[amazon]
[web] |
| Numerical Solution of Stochastic Differential Equations (Applications
of Mathematics, Vol 23) |
Peter E. Kloeden, Eckhard Platen |
[amazon] |
| Matrix Computations (Johns Hopkins Series in the Mathematical
Sciences) |
Gene H. Golub, Charles F. Van Loan |
[amazon] |
| Accuracy and Stability of Numerical Algorithms |
Nicholas J. Higham |
[amazon] |
| Numerical Optimization (Springer Series in Operations Research)
|
Jorge Nocedal, Stephen J. Wright |
[amazon] |
Control Theory
| Title |
Authors |
Link |
| Linear Optimal Control Systems |
by Huibert Kwakernaak, Raphael Sivan (Contributor)
|
[amazon]
|
| Essentials of Robust Control |
Kemin Zhou, John Comstock Doyle |
[amazon] |
| Nonlinear Control Systems (Communications and Control
Engineering Series) |
Alberto Isidori |
[amazon] |
| Nonlinear Dynamical Control Systems |
Henk Nijmeijer, Arjan Van Der Schaft |
[amazon] |
| Stochastic Processes and Filtering Theory |
Andrew H. Jazwinski |
[amazon] |
Dynamical Systems
| Title |
Authors |
Link |
| Dynamics and Bifurcations (Texts in Applied Mathematics, No 3)
|
Jack K. Hale, Huseyin Kocak, Lawrence Sirovich (Editor), Jerrold
E. Marsden (Editor) |
[amazon]
|
| Nonlinear Oscillations, Dynamical Systems, and Bifurcations of
Vector Fields (Applied Mathematical Sciences, Vol 42) |
John Guckenheimer, Philip Holmes, F. John (Editor), Jerrold E.
Marsden |
[amazon] |
| Nonlinear Dynamics and Chaos : With Applications in Physics,
Biology, Chemistry, and Engineering (Studies in Nonlinearity) |
Steven H. Strogatz |
[amazon] |
Stochastic Processes
| Title |
Authors |
Link |
| Stochastic Processes in Physics and Chemistry (North-Holland
Personal Library) |
N. G. Van Kampen |
[amazon]
|
| Handbook of Stochastic Methods : For Physics, Chemistry
and the Natural Sciences (Springer Series in Synergetics , Vol 13)
|
C. W. Gardiner |
[amazon] |
| Markov Processes : An Introduction for Physical Scientists
|
Daniel T. Gillespie |
[amazon] |
| Stochastic Differential Equations : An Introduction
With Applications (Universitext) |
Bernt K. Oksendal, B. K. Ksendal |
[amazon] |
Information Theory
| Title |
Authors |
Link |
| Elements of Information Theory |
Thomas M. Cover, Joy A. Thomas |
[amazon]
|
| Mathematical Foundations of Information Theory |
Alexander I. Khinchin |
[amazon] |
Machine Learning
| Title |
Authors |
Link |
| An Introduction to Support Vector Machines : And Other
Kernel-Based Learning Methods |
Nello Cristianini, John Shawe-Taylor |
[amazon]
|
| Data Mining: Practical Machine Learning Tools and
Techniques with Java Implementations |
Alexander I. Khinchin |
[amazon] |
Statistics
| Title |
Authors |
Link |
| Multivariate Analysis |
K.V. Mardia |
[amazon]
|
| Introduction to Statistical Methods and Data Analysis
|
Lyman Ott, Michael T. Longnecker, R. Lyman Ott |
[amazon] |
| An Introduction to Probability Theory and Its Applications
|
Ian H. Witten, Eibe Frank |
[amazon] |
Nonlinear and Nonequilibrium Chemistry
| Title |
Authors |
Link |
| Chemical Chaos (International Series of Monographs
on Chemistry, No 24) |
Stephen K. Scott |
[amazon]
|
| Statistical Thermodynamics of Nonequilibrium Processes |
Joel Keizer |
[amazon] |
| An Introduction to Nonlinear Chemical Dynamics : Oscillations,
Waves, Patterns, and Chaos (Topics in Physical Chemistry Series)
|
Irving R. Epstein, John A. Pojman |
[amazon] |
Chemical Kinetic Analysis
| Title |
Authors |
Link |
| Chemical Reaction Networks : A Graph-Theoretical Approach |
Oleg N. Temkin, Andrew V. Zeigarnik, Danail Bonchev
|
[amazon]
|
| Enzyme Kinetics : Behavior and Analysis of Rapid Equilibrium
and Steady-State Enzyme Systems (Wiley Classics Library) |
Irwin H. Segel |
[amazon] |
For biologically-minded people:
For most resources you should look at the list above. But there are
a few specialty books that might prove useful to the biologist entering
the field.
Dynamical Systems
| Title |
Authors |
Link |
| Dynamical Systems : A Visual Introduction (Science Frontier Express
Series) |
Frederick David Abraham, Ralph Abraham, Christopher D. Shaw |
[amazon]
|
Bioinformatics
| Title |
Authors |
Link |
| Biological Sequence Analysis : Probabilistic Models of Proteins
and Nucleic Acids |
Richard Durbin (Editor), S. Eddy, A. Krogh, G. Mitchison (Contributor)
|
[amazon]
|
Programming
| Title |
Authors |
Link |
| A Book on C : Programming in C |
Al Kelley, Ira Pohl |
[amazon]
|
| The C Programming Language |
Brian W. Kernighan, Dennis M. Ritchie |
[amazon] |
| Learning Perl (2nd Edition) |
Randal L. Schwartz, Tom Christiansen, Larry Wall |
[amazon] |
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