Advanced Mathematics for Engineering and Science

Advanced Mathematics for Engineers and Scientists
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Bachelor of Science (Advanced Mathematics)(Honours)/Engineering (Honours)

Mathematics in engineering and science. Mathematics in Engineering and Science. Elective course totaling 12 units of credit General Education courses totalling 6 units of credit.

At that time there was no other suitable option for students who were keen to move into Quantitative Risk. However, UNSW now offers a suite of dual degree programs that can offer a wider education for such students. These programs allow a very broad choice of courses that can be tailored for students interested in a career in Quantitative Risk, and so this separate study plan is no longer seen as necessary. The School can provide detailed advice on course choices for UNSW students interested in this field who are not eligible to enter the QR plan.

The books listed here are all calculus based except for the book by Bennett.. An absolutely superb book for the layman, and of interest to the professional accomplishes what many other books have merely attempted. Bennett, Deborah J. See also Tanur. An interesting book, quite philosophical, on randomness is the one by Taleb. One of the best books written for the undergraduate to learn probability is the book by Gordon. Despite the restriction to discrete probability this book is a superb general introduction for the math undergraduate and is very well organized.

Great text!! Gordon, Hugh. Discrete Mathematics. As a rule I think that the best books to learn probability from are those on modeling. For example, perhaps the best writer on probability is Sheldon Ross. Introduction to Probability Models , 6 th ed. Karlin, Samuel. An Introduction to Stochastic Modeling , rev. It is indeed a wonderful book: Hamming, R.

The Art of Probability for Scientists and Engineers. Elementary Probability, 2 nd ed. Problems and Snapshots from the World of Probability. The first volume is inspiring. The larger second volume is even more technical than the first, for example there is a chapter review of measure theory.

Feller, William. Introduction to Probability Theory.

Asymptotic Methods and Perturbation Theory

Vol 2, 2 nd ed. The following is an inexpensive little reference. It requires only a basic knowledge of probability, say through Bayes' Theorem. The great thing about it is that the problems are actually interesting. I have found this to be a good source for classroom examples. Mosteller, Frederick. Fifty Challenging Problems in Probability with Solutions.

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Duelling Idiots and Other Probability Puzzlers. Fuzzy Stuff logic and set theory. Some books in this area are better than others. By in large though, it is a lot of bull about ad hoc, not particularly robust, algorithms. Claims of anything new and profound are general pompous bullstuff.

Fuzzy methods are trivial if you have knowledge of probability and logic. In my view the aspiring applied mathematician can not do better than to study probability. A book of practical statistics as opposed to mathematical or theoretical statistics is the one by Snedecor and Cochran. It is rigorous but does not use calculus.

It uses real life biological data for examples but is fascinating. It is a wonderfully well written and clear book. A real masterpiece. Anyone who actually does statistics should have this book. But remember, though it does not require calculus it does require mathematical maturity. My feeling is that if you want to use this book but do not know calculus you should go back and take calculus.

Snedecor, George W. Statistical Methods , 8 th ed. Iowa State. A great book. The best books about statistics for the layman are very likely: Tanur, Judith M. Statistics: A Guide to the Unknown , 3 rd ed. This is a great book. See also Bennett.

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Applied Functional Analysis. Nicolas Matsuo rated it it was amazing Jul 21, Mehwish Hussain rated it it was amazing Oct 06, Campus Kensington. Paperback , pages.

Salsburg, David. The Lady Tasting Tea. Without using a single formula it does a much better job of telling the layman what statistics is about than does the usual introductory text. It is also of interest to the professional. A classic applied book that is readable and thorough and good to own is: Neter, John, Michael K.

Kutner, Christopher J. Nachtsheim, William Wasserman. Applied Linear Statistical Models, 4th ed. My favorite text on mathematical statistics is definitely the following. It is a large text with enough material for a senior level sequence in mathematical statistics, or a more advanced graduate sequence in mathematical statistics. It is very well done. Dudewicz, Edward J. Modern Mathematical Statistics.

Introduction to the Theory of Statistics. The Cartoon Guide to Statistics. An elementary book that does a nice job on statistical tests and which might be of interest to the practitioner is: Langley, Russell. Practical Statistics Simply Explained. The book by Box, Hunter and Hunter is wonderful at exploring the concepts and underlying theory. The book by Saville and Wood is worth considering by the serious student. Although its mathematics is simple and not calculus based this is the way theory was developed and this is also touched upon in the book by Box, Hunter, and Hunter.

Hicks, Charles R. Fundamental Concepts in the Design of Experiments. Stuart Hunter, and William Gordon Hunter. Saville, David J. And Graham R. Statistical Methods: A Geometric Primer. My favorite book on regression is the one by Draper and Smith. The book by Ryan is particularly elementary and thorough.

Draper, Norman R.

Applied Regression Analysis. Modern Regression Methods. The book by Thompson is for the practitioner. Stuart, Alan. Ideas of Sampling , 3 rd ed. If forced to use time series analysis for purposes of forecasting I almost always will use double exponential smoothing possibly embellished with seasonal attributes and built-in parameter adjusting.

The bible of times series analysis is Box and Jenkins. The book by Kendall and Ord is fairly complete in its survey of methods. I like the book by Bloomfield. Box, George E. Jenkins, Gregory C. Times Series Analysis: Forecasting and Control. Keith Ord. Time Series , 3 rd ed. Edward Arnold. Practical Nonparametric Methods , 2 nd ed. Statistical Distributions , 2 nd ed. The best single book on general operations research is Hillier, Frederick S. Introduction to Operations Research.

Let me mention four. All these discuss the simplex method. I will soon make recommendation s on interior point algorithm books however they are covered in Rardin. A very elementary book that does a great job teaching the fundamentals with pictures is: Gass, Saul I. An illustrated Guide to Linear Programming. Linear Programming.

Integer and Combinatorial Optimization. Integer Programming. Nonlinear Programming. Republication of McGraw-Hill; Optimization in Operations Research. William H. Cunningham, William R. Pulleyblank, Alexander Schrijver. Combinatorial Optimization. It is a book that I would recommend to any student getting into optimization. I think it is a must-have for any serious student of OR. Kaplan, Wilfred. Networks and Algorithms. However, let me mention what I like best: By far the best book for comprehensiveness is: Law, Averill M.

David Kelton. Simulation Modeling and Analysis , 2 nd ed. Carson, II. Discrete-Event System Simulation. Simulation and the Monte Carlo Method. A future edition will cover both decision theory and games of the J H. Conway variety. An early classic of extremely elementary nature is the one by Williams. It precedes the widespread use of linear programming. Williams, J. Dover See Thie. A fine elementary book is: Straffin, Philip D. Game Theory and Strategy. Game Theory , 3 rd ed. Lectures on Game Theory. A well written text at the senior level emphasizing economics is: Romp, Graham.

Game Theory: Introduction and Applications. Stochastic Markov Decision Processes will be covered in a future edition. Stochastic Processes and Queueing. See the first books in probability. A classic that seems out of print is: Parzen, Emanuel. Stochastic Processes.

Schaum's Outline of Advanced Mathematics for Engineers and Scientists

An inexpensive paperback republication of merit is: Ross, Sheldon. Applied Probability Models with Optimization Applications. Dover, Fundamentals of Queueing Theory , 3 rd ed. Queueing Theory: For Services and Manufacturing. Inventory Theory and Scheduling. I am not to smitten with the books in this area. For the second edition I will try to do better. Until then, there is one excellent book in print. There is almost certainly an excellent book to appear. The book by French is excellent and is out of print and shouldn't be. The books by Conway et al and Hadley et al were published in the sixties and are out of print and despite that are first rate if you can get your hands on them.

The book to have these days: Silver, Edward A. Pyke, and Rein Peterson. Inventory Management and Production Planning and Scheduling , 3 rd ed. So I would bet this will be a must have book for its area: Lawler, E. Lenstra, and A. Rinooy Kan. Theory of Sequences and Scheduling. Scheduled for A book that never should have gone out of print: French, Simon. Ellis Horwood. Maxwell, and Louis Miller.

Theory of Scheduling. Analysis of Inventory Systems. Introduction to Sequencing and Scheduling. This is a new area for me. There are a lot of books giving contradictory advice or useless advice. Investment theory is inherently mathematical, but there is a mathematical offshoot known as "technical analysis. Some of it is as bad as astrology. The better technical analysis stuff is basically a dead end, or perhaps I should say deadly end.

The book by Malkiel aresses it well. General Physics. I really haven't gotten around to this area yet. Secondly, I prefer to learn most physics from specialized sources for example to study mechanics, how about using a book just on mechanics? One series you are sure to hear about is the great series by Feynman.

Be aware, that it is probably more useful to people who already have a knowledge of the subjects. Also, it is a great reference. It deserves its reputation as a work of genius, but in gneral I would not recommend it to someone just beginning to learn physics. There is a great classic, very readable, by a major thinker, full of history, that goes back to Mach, Ernst. The Science of Mechanics , 6 th English ed. Open Court. Classical Mechanics. University Science Books. Newtonian Mechanics. A couple of concise well written first books for the student who has been through the calculus sequence: Smith, P, and R.

Mechanics , 2 nd ed. A First Course in Mechanics. Classical Mechanics , 4 th ed. Very nice!! Elements of Newtonian Mechanics. Classical Mechanics: A Modern Introduction , 2 nd ed. Woodhouse, N. Introduction to Analytical Dynamics. A couple of thorough books: Greenwood, Donald T. Principles of Dynamics , 2 nd ed. Textbook of Dynamics , 2 nd ed. Wiley actually it is not clear who published this. Three undergraduate books in order of increasing difficulty: Chorin, Alexandre J.

A Mathematical Introduction to Fluid Mechanics , 3 rd ed. Topics in Fluid Mechanics. Fluid Mechanics. Thermodynamics and Statistical Mechanics. There are several books for laymen on the second law of thermodynamics. The first by Atkins is well illustrated--basically it is a coffee table book. Atkins is one of the best science writers alive. The book by the Goldsteins does a thorough job of discussing the history and concepts of thermodynamics. It is also very good. Atkins, P. The Second Law.

Four Laws that Drive the Universe. Goldstein, Martin, Inge F. It is probably of less interest to nerds. An unusual book in format that is aimed at the serious student, but is definitely worth having: Perrot, Pierre. A to Z of Thermodynamics. The Physics of Chance.

Basic Engineering Thermodynamics. Understanding Thermodynamics. The book by Lawden is fairly brief. Lawden, D. Principles of Thermodynamics. Statistical Physics: A probabilistic Approach. Classical and Statistical Thermodynamics. Electricity and Electromagnetism. An elementary "coffee table" book would be: Fowler, Richard J. Electricity: Principles and Applications , 4 th ed. Also, another fine book with Schey in the section on Vector Calculus is the book by Marsden and Tromba.

Unless my memory is suffering the ravages of alcohol, the 4 th edition has a much more thorough treatment of Maxwell's equations of electromagnetism than did the 2 nd edition. A book for people interested in electrical engineering and who want a single book to get them into it is: Rutledge, David. T he Electronics of Radio. A truly excellent short book; a must have for students of EE. Highest recommendation: Fleisch, Daniel.

A Students Guide to Maxwell's Equations. Lancaster, Gordon. Introduction to Fields and Circuits. The book by Skilling is a reprint of an ancient work and is highly recommended. Skilling, Hugh H. Fundamentals of Electric Waves. Dugdale, David. Essentials of Electromagnetism. American Institute of Physics. Schwarz, Steven E. Electromagnetism for Engineers. Cottingham, W. Electricity and Magnetism. Westgard, James Blake. Electrodynamics: A Concise Introduction. Electricity and Magnetism , 2 nd ed. Electromagnetism: Principles and Applications , 2 nd ed.

Engineering Electromagnetics. A book which I think is particularly well written and clear: Dugdale, David. Engineering Field Theory with Applications. Quantum Mechanics. There are books that try to explain quantum physics to the layman, i. For the most part it is like trying to explain Rembrandt to a person who has never possessed sight. To start off with I'll mention one of the non-mathematical coffee-table works: Hey, Tony and Patrick Walters. The Quantum Universe. Ponomarev, L. The Quantum Dice. Institute of Physics. Quantum Mechanics and Experience.

Quanta: A Handbook of Concepts , 2 nd ed. Primer of Quantum Mechanics. Introduction to Quantum Physics. Wolf, H. An Introduction to Quantum Physics. The Meaning of Quantum Theory. Quantics: Rudiments of Quantum Physics. North Holland. A much more comprehensive treatment that can be a little hairy but nonetheless is as readable as this stuff gets: Zee, A. Quantum Field Theory in a Nutshell. Bell, J. Speakable and Unspeakable in Quantum Mechanics. It is however rather subtle and deserves a lot of attention. A literature professor would explain that the special relativity is a nuanced paradigm reflecting in essence Einstein's misogyny.

As to general relativity it can not be understood with little more than algebra. Rather, it can be described technically as a real mother-lover. On the subject of general relativity and covering special relativity as well, there is a magnum opus, perhaps even a 44 magnum opus. This book is the book for any serious student. I would imagine that graduate students in physics all get it. It is pages long and it takes great pains to be pedagogically sweet.

Tensors and everything are explained ex vacua that is supposed to be Latin for out of nothing it probably means death to the left-handed. I have trouble seeing this all covered in two semesters at the graduate level. It is formidable but it is also magnificent. Misner, Charles W. The only caveat here is that there are many fine books on special relativity and some of them are less technical. Nonetheless the book avoids calculus.

Taylor, Edwin F. Spacetime Physics: Introduction to Special Relativity , 2nd ed. Although it can be read independently, I strongly recommend reading Spacetime Physics first. Epstein, Lewis Carroll. Relativity Visualized. Insight Press. Special Relativity. Einstein's Theory of Relativity. Born was a Nobel laureate. Rindler, Wolfgang. Introduction to Special Relativity , 2 nd ed. The last two Harpaz and Hakim are very mathematical and in my judgement Harpaz is the more elementary of the two.

The book by Bergman is wonderfully concise and clear. Gibilisco, Stan. The Rile of Gravitation. General Relativity from A to B. University of Chicago. Relativity Theory: Concepts and Basic Principles. An Introduction to Relataivistic Gravitation. Seuss with tensors. Lieber, Lillian. Paul Dry Books. The best introduction I think is: Pierce, J. Almost All About Waves. Pierce is a great expositor. Vibrations and Waves. Vibrations and Waves in Physics , 3 rd ed. Also, it covers more topics and applications than the others.