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Here are a few mathematics resources that I have found useful.

Introduction to Complex Analysis: WWL Chen
http://www.maths.mq.edu.au/~wchen/lnicafolder/lnica.html
This is very clearly written and better than most books I have read. The explanations and examples really stand out.

Complex analysis and Functional Analysis: Douglas N. Arnold.
http://www.ima.umn.edu/~arnold/502.s97/complex.pdf
http://www.ima.umn.edu/~arnold/502.s97/functional.pdf
2 excellent documents. The first is probably a little more accessible than the second which requires a substantial mathematics background.

A First Course in Complex Analysis: Beck, Marchesi and Pixton
http://math.sfsu.edu/beck/papers/complex.pdf

First Course in Linear Algebra
http://linear.ups.edu/download.html

Cauchy-Schwarz Master Class: by J. Michael Steele
Whilst this book is not free, several sample chapters are downloadable (http://www-stat.wharton.upenn.edu/~steele/Publications/Books/CSMC/CSMC_index.html ). A truly remarkable book whose clarity and insight is a rarity amongst such books, which often gloss over details and leave the reader baffled. Although a specialised work, I have come across very few mathematics books that can equal it as an educational tool. If you are about to embark on a postgraduate Mathematics (or indeed undergraduate) course of study make sure you read this book.

List of Free Mathematics Books: a great resource!
http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html
This should be your first port of call if you are looking for free online material.

There is another list of free online Textbooks here: http://linear.ups.edu/opentexts.html

Introduction to Tensor Calculus and Continuum Mechanics
http://www.math.odu.edu/~jhh/bookpdf.zip
by John H. Heinbockel

Concrete Mathemathics, 2nd Edition. (aimed at CS postgraduate students)
http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025
Not a free book, but if you are about to pursue Computer Science postgraduate studies in algorithmics, complexity analysis or a related subject, then this work is required reading.

If you know of any other high quality work, free or otherwise, please let me know.

Patrick Smacchia at NDepend let me know that new trial and PRO versions of NDepend (2.4) , the code metric and dependency tool, are now available. They have been working hard on simplying the interface and making it more intuitive. One of the things I love about NDepend is that it has its own TSQL-like query language built in! There are a few new tutorials posted as well.

If you want to get the flavour of an O’Reilly book before you buy it, there is a list of their most recent sample chapters here (most recently available chapters are at the top of the list). You can find additional sample chapters by browsing O’Reilly’s Book List.

O’Reilly also has an open book project that is worth checking out.

Having decided that I couldn’t put up with Adobe Acrobat gremlins and infuriating prompts to download the next version any longer, I remembered FoxIt, a lightweight PDF reader. Not sure how I arrived there, but I found it listed at this wiki site that also lists a plethora of free software and utilities.

Nothing new, just wanted to remind myself that they can be found here!

You have probably seen the “What am I doing to be a better programmer in the next 6 months” developer meme that has been doing the rounds. Along with the advice “Read more technical books”, one of the common themes is that you should read others people’s code, and lots of it!

Reading code is a great way to improve your code writing skills. This is something that I believe in, and I have to admit I’m guilty of not reading enough of other developers’ code. Find an open-source project or a developer whose work you respect, and read the code. Look for idioms and patterns, learn from their experience. I believe undergraduate computing courses should offer a course which consists of dissecting and understanding code written by prominent coders.

Scott Hanselman has a great post on the topic here, where he mentions the Coding4Fun developer kit, a great resource for learning from other people’s code.

Jeff Atwood’s post How To Become a Better Programmer by Not Programming is worth a read, if you have not seen it already.

I recently reviewed the book “Beautiful Code” from O’Reilly, a collection of articles, essays and papers from many talented programmers. It provides insights and techniques that would be hard to arrive at if you had to reinvent them yourself. There is also a dedicated web site here: http://beautifulcode.oreillynet.com/.

For a glimpse into the mind of one of Computer Science’s well known contributors, check out the “Edsger W. Dijkstra” archive (mentioned at the Beautiful Code site): http://www.cs.utexas.edu/users/EWD/

Came across this post by Scott Berkun several weeks ago, and it slipped off my on-post list!:
How to write a book – the short honest truth

I came across this MSDN article (May 2006) by Stephen Tolub on Managed Debugging Assistants (MDAs), a CLR feature I was unaware of. Useful article, especially if you are doing any P/Invoke work. MDAs “…provide information on the CLR”s current runtime state and on events that you as a developer could not otherwise access. Some even modify runtime behaviors to help expose otherwise very hard to find bugs.”

There is a listing of all Stephen Tolub’s MSDN articles here.

And I’m not talking about Sydney APEC conference! Last night’s Perth .NET user group presentation with speaker Nick Wienholt was excellent, and we had another great turnout (I counted 47 people). Here are a few photos of the meeting:

1. Logic: Introduction
2. Set Theory: Introduction
3. More Logic
4. Relations and Functions
5. Tables and Database States
6. Tuple, Table, and Database Predicates
7. Specifying Database Designs
8. Specifying State Transition Constraints
9. Data Retrieval
10. Data Manipulation
11. Implementing Database Designs in Oracle
12. Summary and Conclusions

If you’ve studied mathematics (or a tertiary subject with a mathematics element to it) you will most probably be familiar with the sections on set theory and logic. If you have not then they provide an as excellent introduction to these topics that you are likely to find anywhere.

This book makes the following claims and I have made comments against each one:

“This book will help you”:

• “Become a better database designer. You’ll make fewer mistakes, and your designs will be more flexible in response to changing data needs.” I agree 100% that having a good, if not intuitive, grasp of logic and basic set theory will help you to create better DB schemas.
• “Use the expressive power of mathematics to precisely specify designs and business rules.” I am not sure how useful this is, and I have a mathematics background. I personally feel that having another notation to express the database design seems to break the DRY (Don’t Repeat Yourself) principle.
• “Communicate effectively about design using the universal language of mathematics.” I personally do not think this applies unless you are at the top of your game and/or have a theoretical bias and you are communicating with someone similar.
• “Develop and write complex SQL statements with confidence.” Absolutely agree. I am often surprised at the number of software developers that do not have a thorough grasp of logic.
• “Avoid pitfalls and problems from common relational bugaboos such as null values and duplicate rows”. Probably, but then 3NF will go a long way to achieving that.

I would be the first to agree that a good, basic mathematics grounding is desirable if you want to confidently design databases that scale well and are modelled correctly.

The mathematics that you learn in this book will certainly put you above the level of understanding of most database professionals. But I am not convinced that alone will enable you to better understand the technology and be able to apply it more effectively. It will help you to avoid data anomalies like redundancy and inconsistency, which are not uncommon problems in the world of databases!

On the whole, I enjoyed reading this book, but I’m not sure if I learnt anything I could immediately put to use when designing and refactoring databases. I did not put a great deal of effort into learning and understanding the formal database specification language described in this book purely because I could not see an immediate benefit when balanced against the effort required to learn a new notation, and I may well have overlooked something crucial that would indeed enable me to create better database designs.

Disclosure: The Perth .NET User Group is a member of the Apress User Group Program. Apress make copies of their books available for user group libraries, and the copy reviewed here was kindly donated by them.