# shah_nosrat

Senior Members

44

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• Rank
Quark

## Contact Methods

• Website URL
http://floatingbicycles.blogspot.com

## Profile Information

• Interests
Mountain Biking
• College Major/Degree
University of South Africa
• Favorite Area of Science
Mathematics and Philosophy.
• Biography
Studying a BSc(Mathematics)
• Occupation
Student
1. ## Show that f is 1-1

There's a mistake in your equality; it's supposed to be $2xy^2 - y^2 + y = 2yx^2 - x^2 + x$, factoring both terms on each side of the equality we have: $y(2xy -y + 1) = x(2xy -x + 1)$, which we can argue for x to equal to y we should have $2xy -y + 1 = 2xy - x + 1$, which reduces to $x=y$ as required, hence, your function is injective.
2. ## Linear Algebra

From what I studied in discrete mathematics, relations have matrix representations, and besides the operations we are used in linear algebra, there are also boolean operations that can be performed on matrices.
3. ## 2 Questions Concerning the Basics

I don't understand your vector representations. But from the definition of linear independence, it says the following, that the linear combination of the vectors; k_{1}v_{1} + k_{2}v_{2} + k_{3}w = 0, if k_{1}=k_{2}=k_{3}=0 solving this equation will give your solution.
4. ## Why is it called "linear" algebra?

Just to answer your last statement. Abstract Algebra deals with the study of mathematical structures called groups. To give an example between LA (Linear Algebra) and AL (Abstract Algebra) on their similarity (not in property, but on the approach, since it's algebra). In LA we have basis sets that spans a particular vector space, and how an entire vector space can be constructed by the basis set. Similarly in AL we have cyclic sets that generates an entire group! So their approach is similar, but as John puts it: that's why is called Linear Algebra. Besides, LA has immense applic
5. ## shah_nosrat

It's been a while......now I'm back!!!!

1. Welcome back!!!

6. ## Comprehensive Mathematics for Computer Scientists 1

I haven't read the above book. But I do know that any computer scientist needs to have knowledge of Discrete Mathematics: As this will teach you naive set theory, logic, counting principles, Relations, Digraphs, Graph theory, Languages and finite - state machines and much more. Then you could complement it with the above mentioned book. When dealing with Definitions, axioms, theorems, and proofs. It's always a good idea to understand what a particular definition, axiom or theorem is saying and then going on to reading the associated proof to get a complete picture of whats going on
7. ## Who are some of the top mathematicians, currently

Edward Witten Michio Kaku Andrew Wiles Stephen Hawking Roger Penrose Yes some of the above are Theoretical Physicists, but as ajb put it, they did spur modern mathematics.
8. ## robots as a species

I don't know if considering robots as its own species would be a good idea, not to mention it being an intellectual being/entity. We would then have to consider their robotic rights as well, and would give rise and debate to ethical considerations of how to deal with these new robotic beings or their species as a whole. But I do know that Japanese scientists creating realistic humanoid robots to assist us in our daily chores or life for that matter, they consider it as being the next evolution of the so-called "Personal Computer". Now to consider something as alive, they would have to
9. ## Suggestions for books that talk about good ways to teach a young child science, etc.?

Hi, try some books by Stephen Hawking: George's Secret Key to The Universe, and other science books for Kids. I don't know if they improve critical thinking, but it sure will encourage imagination and creative thinking in kids, which is also important in any field of science.

13. ## What are you listening to right now?

Seattle's Calling - by Burn The Charts
14. ## Well Ordering Principle: Proof

Hi, This is the question that needs a proofs, as follows: Show that the smallest element of a nonempty subset of $\mathbf{W}$ is unique. My attempt at the proof, as follows: Let $\mathbf{U} \subseteq \mathbf{W}$, by the well ordering principle (WOP) we have that $a \in \mathbf{U}$ such that $a \leq x$ $\forall x \in \mathbf{U}$. Now suppose $b \in \mathbf{U}$ such that $b \leq x$ $\forall x \in \mathbf{U}$. Since $0 \leq x - a$ and $0 \leq x - b$ by definit
15. ## Advice for sharpening my math skills

First of all keep the doubts and negative thinking aside. I believe that anyone is capable of great things as long as they're interested. If you are interested in Higher Mathematics then that's the first step to learning Higher Mathematics. Let me tell you this, that Higher Mathematics trains you to think analytically and critically about any problem presented to you. And remember to always have fun
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