Out of all the maths I have used, linear algebra seems to be the most useful in computer science. Unlike calculus, which I have yet to see many applications for in this field. Things taught to me in linear algebra just seem to be used a lot more than those in calculus.

1.a) a method of computation or calculation in a special notation (as of logic or symbolic logic)

Maybe we're just doing some very different things in these subjects, but can you give me an example of when Linear Algebra (beyond the very very basics that don't really merit any real study of the subject) has been helpful in CS?

Now, do you mean that by graphics? And if so, I could see the possibilities of Linear Algebra being involved with 3D graphics, but with 2D? Either way, it's very interesting stuff.

Linear Algebra is used in cryptography to if some block chyphers are secure or not as well as in some chypers that use matrixs. It is also used for anything invovling matrixs and vectors witch inclues graphics and phsyics applications (Both 2d and 3d, vector graphics, photoshop, ect for 2d).

Math is also very imporent in determining the effshentys of alrogithms in terms of both time and memory. However as CPUs and computers become more powerfull the relevence of it will become less.

a computer scientist that's not necessarly good at math might be better at working in a team environment, working well with others, great at graphics, or even writing documentation, while the one that is good at math might have trouble with dealing with other people, writing, or designing graphics. I'm not saying that's the case, but I have seen stuff like this occuring here in my first year of uni. *shrugs*

Hardware advancements are no excuse for writing poor code. besides hardware is already hitting a limit point. processors are getting overheated so they are using multiple cores to compensate. not before long that'll fail too

that is completely stereotyping. I've worked with a graduate in PM that works at a leading graphics company. he is one of the smartest guys I met, writes excellent graphics code and a very outgoing person and team player.

what kind experiences do YOU have?

I'd watch it if i were you. You don't want to end up looking in 10 years like the guy who said no computer would ever use more than 64kb of RAM. The only implication of what you say is that we need to develop better cooling technologies. It is not a limit on how fast processors can get.

He did use the word "might"...and also said "I'm not saying that's the case".

actually security in crypto systems doesnt come from linear algebra. it involves more using group and ring theory, as well it comes from complexity theory that certain problems are difficult to solve efficiently. In fact it goes under the motto "if nobody can break this, then it must be security", for the reason that it is often very difficult to prove that a certain problem is hard to solve (ie the P=NP problem)

If a problem takes 10 million years to solve, no matter how fast you make your computer, you still won't get it down to a few seconds. Hardware advancements are no excuse for writing poor code. besides hardware is already hitting a limit point. processors are getting overheated so they are using multiple cores to compensate. not before long that'll fail too

i wasn't ever suggesting on whether block cipher uses linear algebra or group theory. the point is not that cryto algorithms can be broken by a certain method, the point is that a cryto system is security ONLY IF all known algorithms to break it would not finish in this life time, even when run on supercomputers or distributed networks.

quantum computing solves two problems: deutsch's algorithm and grover's algorithm. AGAIN algorithms are used to attack problems, NOT hardware speedup. aside from that, quantum computer has no superiority over traditional computers.

quantum computing solves two problems: deutsch's algorithm and grover's algorithm. AGAIN algorithms are used to attack problems, NOT hardware speedup. aside from that, quantum computer has no superiority over traditional computers. bottom line? hardware gives you at most linear speedup. 10 years from now, computers maybe 10 times faster, but that really means nothing.

As a side question...I was under the impression that you could use a QC to solve shortest-path problems. Is this true?

I dont know of any quantum algorithm that solves the shortest path more efficiently than a normal computer.

to tell you the truth i have no idea how to attack a block cipher, and honestly i doubt you know how it works either.

quote you was just saying comments related to the topic. on the other hand, i've taken lectures in quantum computing, and I know you have absolutely no idea what you are talking about there.

and to say that code efficiency is not important due to hardware speedup is definitely a misconception.

thats like putting a disclaimer. im telling him that he is wrong and it is definitely not the case and that he was stereotyping.

Stuff

This is a fascinating topic. What an interesting read. On a side note, I found an article about How to Become a Hacker today (Rather a guide). Its very interesting to read and can be found here: http://www.catb.org/~esr/faqs/hacker-howto.html. After reading this forum, I can't but help pointing something out. Is it me or does Hacker Dan have horrible English writing skills? I don't doubt he's a very intelligent person. I don't doubt that he probably knows a lot about computer science and hacking. I'm not saying I have perfect literary skills. I just want to point out the 4th Basic Hacking skill as found in that guide. (4. If you don't have functional English, learn it.) I just can't read any of his writing. If you are reading this, Hacker Dan, may I offer you some advice from a humble forum member: Learn proper grammar. In computer science, or rather in hacking, in general, knowing proper grammar is very important. Read over the 4th point in the guide. I agree with the fact that no matter how intelligent you are, if you can't write, fellow hackers are just not going to listen to you or take you seriously.

Before the 1920s, computers were human clerks that performed computations. They were usually under the lead of a physicist. Many thousands of computers were employed in commerce, government, and research establishments. Most of these computers were women, and they were known to have a degree in calculus. Some performed astronomical calculations for calendars.

After the 1920s, the expression computing machine referred to any machine that performed the work of a human computer, especially those in accordance with effective methods of The Church-Turing Thesis. The thesis states that a mathematical method is effective if it could be set out as a list of instructions able to be followed by a human clerk with paper and pencil, for as long as necessary, and without ingenuity or insight.

Machines that computed with continuous values became known as the analog kind. They used machinery that represented continuous numeric quantities, like the angle of a shaft rotation or difference in electrical potential.

Digital machinery, in contrast to analog, were able to render a state of a numeric value and store each individual digit. Digital machinery used difference engines or relays before the invention of faster memory devices.

The phrase computing machine gradually gave away, after the late 1940s, to just computer as the onset of electronic digital machinery became common. These computers were able to perform the calculations that were performed by the previous human clerks.

Since the values stored by digital machines were not bound to physical properties like analog devices, a logical computer, based on digital equipment, was able to do anything that could be described "purely mechanical." Alan Turing, known as the Father of Computer Science, invented such a logical computer known as the Turing Machine, which later evolved into the modern computer. These new computers were also able to perform non-numeric computations, like musi.

From the time when computational processes were performed by human clerks, the study of computability began a science by being able to make evident which was not explict into ordinary sense more immediate.

The theoretical groundwork

The mathematical foundations of modern computer science began to be laid by Kurt Gödel with his incompleteness theorem (1931). In this theorem, he showed that there were limits to what could be proved and disproved within a formal system. This led to work by Gödel and others to define and describe these formal systems, including concepts such as mu-recursive functions and lambda-definable functions.

1936 was a key year for computer science. Alan Turing and Alonzo Church independently, and also together, introduced the formalization of an algorithm, with limits on what can be computed, and a "purely mechanical" model for computing.

These topics are covered by what is now called the Church–Turing thesis, a hypothesis about the nature of mechanical calculation devices, such as electronic computers. The thesis claims that any calculation that is possible can be performed by an algorithm running on a computer, provided that sufficient time and storage space are available.

Turing also included with the thesis a description of the Turing machine. A Turing machine has an infinitely long tape and a read/write head that can move along the tape, changing the values along the way. Clearly such a machine could never be built, but nonetheless, the model can simulate the computation of any algorithm which can be performed on a modern computer.

Turing is so important to computer science that his name is also featured on the Turing Award and the Turing test. He contributed greatly to British code-breaking successes in the second world war, and continued to design computers and software through the 1940s, but committed suicide in 1954.

At a symposium on large-scale digital machinery in Cambridge, Turing said, "We are trying to build a machine to do all kinds of different things simply by programming rather than by the addition of extra apparatus".

In 1948, the first practical computer that could run stored programs, based on the Turing machine model, had been built - the Manchester Baby.

In 1950, Britain's National Physical Laboratory completed Pilot ACE, a small scale programmable computer, based on Turing's philosophy.

The NOTION of an algorithm is basic to all of computer programming... --Donald E. Knuth

hmm... the above post explains it:P But anyway, I know that the prefix Hacker doesn't mean someone who knows how to break security. The guide that I posted the link to doesn't explain how to become a hacker as in someone who knows how to break security. It explicitely states that such a person is better called Cracker. Anyway, sorry for getting off topic. Back to mathematics and Computer Science.