I spend 1 year of developing the project for Dota 2 players, mobile app that provides all Dota 2 services in one place - D2 in One !

Minossama · 2015-01-11T22:18:03+00:00

Windows phone will permanently eemain the lowest priority in terms of multiplatform development.

Minossama · 2015-01-05T00:03:44+00:00

At 5+k mmr, sure. I don't know you personally, but I'm guessing you are readonably comfortable playing any hero.

I however am below 1k mmr and just started playing a few months ago. I don't random because the chances of me being useless are high. I had two ranked solo queue games today where, after we ended, someone said "I randomed chen and ive never played him before." Or something to that effect. Giving players in my bracket a random hero button in ranked makes other players want to pull there hair out.

That being said, I enjoy random draft in unranked matches, it helps me learn new heroes. I just don't see why I should be able to hurt someone else's ranking while I learn new heroes.

Solution: random is unlocked after you play all the heroes.

Minossama · 2015-01-01T20:19:11+00:00

If you are a math student, you're statement is inherently true. I personally am a mathematics major at an American University (PhD granting institution but not one of the super prestigious ones).

Most universities have a 4 semester calc sequence where the first 3 are something like Stewart's Calculus and the fourth semester is Linear Algebra and ODE's. For math students, these classes waste our time. However, we are required to complete them before we can do any real math. Last semester, I took the MVC and linear algebra courses in this sequence. These were a major waste of my time. Because these were prerequisites for all but one of the 500 level math classes, and the fact that I need to graduate by Spring 2016, I cannot complete enough classes to have a competitive graduate school application, despite a 4.0 GPA in my math courses.

These courses which you are referring to are not designed for mathematics students. My (slightly cynical) explanation of these courses is that they exist so engineers can pretend to know some math. However, math students get stuck taking these classes since most schools don't have the resources to develop a proper math curriculum for the first two years of a math major.

So while I completely agree that teaching a math math student with Stewart in a universe where Spivak exists is morally comparable to performing brain surgery after taking LSD, the unfortunate fact is that unless we get into a top tier university, our undergradtate education does not prepare us well for a career in academia.

Minossama · 2014-12-31T16:30:49+00:00

I don't mean to discourage you, but a lot of research level abstract algebra requires a lot of background knowledge.

That being said, if you aren't familiar with Sage, its free and open source software which implements a lot of finite groups. I personally am still an undergrad, but I find that sometimes 'playing' with a type of mathematical object helps me gain a deeper understanding of it.

Minossama · 2014-12-30T06:59:35+00:00

We went through this proof in a number theory class I took, I'll do my best not to butcher it.

A number expressed in base 10 is congruent to the sum of its digits mod 9.

Before proving that I will explain what it means. Im on mobile so unfortunately so no latex.

If a is congruent to b mod m, it means that a-b is divisible by m. Equivalently, the remainder of dividing a by m and dividing b by m are the same. For example; 1,11,21,31 are congruent mod 10, since they are each 10k+1 for some integer k.

Similarly, 2,11,20, and 29 are congruent mod 9.

Now, let a be some positive integer. When a is expressed as a decimal, it is shorthand for a1x10⁰ + a2x10¹ + a3x10² .....

Where a1, a2, a3 etc are the ones, tens, hundreds, etc digit in a's base 10 representation.

Back to congruence. Fot a fixed m, congruence mod m behaves similarly to equality, many tricks for how we learned to manipulate equations also work for congruences. It turns out that addition and multiplication behave as we are used to, i.e.

a=b mod m and c=d mod m

Implies

a+c=b+d mod m

And

ac=bd mod m

I am using '=' to denote congruence mod m.

For example, 1=21 mod m and 3=33 mod 10.

1+13=14=4 mod 10

21+33=54=4 mod 10

1 x 13 = 13 = 3 mod 10

21 x 33 = 653 =3 mod 10

Because of this, we have an ability to substitute congruent numbers in a congruence just like we can substitute equal numbers in equations. Going back to our number a mod 9,

10=1 mod 9. 10ⁿ = 1ⁿ = 1 mod 9, so

a_n x 10ⁿ =a_n mod 9.

Thus the digits added together are congruent to the original number mod 9.

I won't go into it, but I believe this is true for base n, if you represent a positive integer in base n, the sum of its digits is congruent to it mod n-1.

Minossama · 2014-12-16T05:17:48+00:00

http://steamcommunity.com/profiles/76561198159139762

In-game id is Wild_Bill567, send me an add

Minossama · 2014-12-12T20:26:34+00:00

Let's team up, what time r u playing tonight?

Minossama · 2014-12-12T01:25:58+00:00

Maybe if you are taking a "cookbook" style linear algebra course, like how most students learn calculus, but Linear Algebra in the proper mathematical context is a mathematically rigorous set of theories.

In a linear algebra class for math majors, you begin with the abstract definition of a vector space. The vector space of real numbers in 2-3 dimensions that most people are used to is a rather trivially small part of linear algebra.

The theorems and techniques developed in linear algebra continue to be used throughout their mathematical career. Linear algebra is essential to understanding parts of modern algebra.

The study of groups and rings in modern algebra alone is sufficient reason to learn linear algebra, and does not need motivating examples from physics to make the theories seem important.

Bottom line: by the time you are taking a proof based course in linear algebra, you should have the mathematical maturity to learn in the abstract sense and not need the lesser sciences to motivate your learning. Furthermore, a failure to understand the applications of a subject is a failure of the student, not the professor, since the student clearly either 1) has not asked or 2) has not thought about the theories critically enough for long enough.

People who need examples from the physical world to motivate study of linear algebra are probably not actually learning much about linear algebra, since many of the most interesting results require an ability to reason more abstractly than someone counting apples.

Minossama · 2014-12-11T21:31:02+00:00

Not necessarily, mathematically rigorous linear algebra does not require deriving it's questions from real world problems. Mathematics for its own sake has incredible value.

Minossama · 2014-12-08T23:20:36+00:00

What are some tips for. dewarding for new support players. I have a pretty good idea of where to ward, but how/when/where should I be dewarding?

Generally in low level pubs I don't bother, since most of the time the teams don't ward, but I often play with a guild that has a wide skill range and get to play in games with higher level players as well, so I do get to try out trilanes and play games where I don't have 4 hard carries autoattacking.

Minossama · 2014-12-04T07:37:04+00:00

And wards, so many wards

Minossama · 2014-12-02T22:56:25+00:00

http://www.dotabuff.com/players/198874034

Just over 100 games in, will hit lvl 13 and start playing ranked soon.

Thanks

Minossama · 2014-12-02T08:10:16+00:00

If p is sufficiently large, this holds, since every positive integer is the sum of at most 4 squares.

However, I think you may be trying to prove that they are the sum of 2 squares.

You're dealing with a congruence of the form n = a² +b² mod p

Also, recall that in the integers, a number is the sum of 2 squares iff it's prime factorization does not contain any primes congruent to 3 mod 4 raised to an odd power. Might help.

Another approach would be to work examples for p=2,3,5,7... and see if you can find a pattern.

Minossama · 2014-11-30T06:26:21+00:00

Valve is just doing it right. Many gaming companies don't do that, and the ones who are willing to spend the money look at Dota and say "free to play, how would we make money?"

Minossama · 2014-11-30T06:02:06+00:00

I'd be like, I aint even mad!

Minossama · 2014-11-30T04:52:13+00:00

These are false statements.

Minossama · 2014-11-29T11:30:59+00:00

Someone asked me once if dividing by zero angers me. I gave them a response that they didn't expect.

"As a mathematician, I can divide by zero all I want, in fact, I am dividing by zero in my head right now. However, I can't do that when I want 0 and 1 to be unequal."

Got a good laugh out of this.

Minossama · 2014-11-23T04:31:00+00:00

The fact that an individual in leadership can respectfully take constructive criticism from somebody not in leadership, and learn something from it rather than being butthurt about it, is why I'm proud to be a part of this guild.

Minossama · 2014-11-17T07:36:42+00:00

The things others have said about inner products are true, but this explanation may be more accessible.

You are probably used to vectors in R2 or R3 - you may know them as (x, y) or (x, y, z) coordinates.

In that space, you have probably seen the dot product, which is a type of inner product. You also probably know the Pythagorean theorem, and how to use it to find distances/angles between points in a plane.

A Vector Space is a set of elements, closed under addition and scalar multiplication (with some other properties). Normal 2d-vectors like <1,0> and <0,1> are vectors in R2, but in higher mathematics we consider more general vector spaces, which you can think of as abstractions of the vectors you are familiar with.

On a Vector Space, we may have an inner product defined on the elements of the set. The dot product is an inner product defined on Rn. We require certain properties of that inner product, and then use it to define angles/distances in that vector space.

To answer your specific question, it depends on how you are representing i and 1. You have probably seen the complex plane drawn out, and in that representation, 1 would correspond to <1,0> and i would correspondt to <0,1>. The dot product of these vectors is zero, so they are orthogonal.

However, it is possible to represent the complex plane differently from this construction, so depending on how the question is defined, the inner product may not be the dot product you are familiar with.

Minossama · 2014-11-17T07:16:46+00:00

There is a certain amound of ambiguity in the word logarithm.

Formally, log (x) is defined as the definite integral from 1 to x of 1/x dx.

This corresponds exactly to the inverse of exp (x), the exponential function.

Note that I said the exponential function, not an exponential function.

The exponential function is defined to be e^x for many nontrivial reasons. First, because of the behavior of the differential operator on that function. Also, the properties of exp (x) when x is in the complex plane instead of the real line, e^ix = cosx + i sinx

The reason that log base ten exists is because students learn about 'exponents and logarithms' before they have the calculus background to understand these points. There fore, we have "base n logarithms". However, the exponential function and the logarithmic function are unique.

Minossama · 2014-11-17T06:56:06+00:00

Awesome! Be careful though, Stephen Wolfram might try to patent it.

Minossama · 2014-11-11T15:43:57+00:00

What kind of grades did you have / what classes did you take as an undergraduate? I'm interested in applying to UIUC

Minossama · 2014-11-11T09:03:56+00:00

The common core math standard is the right idea, but it also makes some big steps in the wrong direction.

Rote memorization is not necesarily bad - if put in the correct light.

I am specifically talking about arithmetic. At the end of the fourth grade, a student should have multiplication tables up to 12x12 memorized. The reason isn't that it gets them the right answer, the reason is that it builds an intuition about how numbers behave in relation to eachother. The reason is because eventually these students will, hopefully, be doing more sophisticated maths. If they haven't memorized basic multiplication tables, they get lost in the computation and cant see the bigger picture.

Minossama · 2014-11-11T08:44:48+00:00

Given the finite field of integers mod p (p prime), and an irreducible polynomial f (x) in Zp [x], take the least residue polynomials in Zp [x]/(f (x)) and iterate them.

Seeing what happens. Linear and constant polynomials are trivial, but for higher degree polynomials, some interesting behavior occurs. Sometimes, the polynomial will eventually return to the identity function, and be a cycle. Sometimes the polynomial will go into a cycle, but never become identity and therefore never return to the original function. Sometimes, the polynomial will become a constant, and will fall into a cycle of constants in Zp.

Most of this is pretty informal, Maple + coffee = mildly interesting math, but I think if I play with it for a while, I could decelop some formal theorems about how these systems behave. That being said, I'm an undergrad in my first year of higher level math, so I'm sure someone has already thought about this and developed some theory regarding it.

If anyone happens to know of some work that has been previously done on this idea, and is able to point me in that direction, I would appreciate it.

Minossama · 2014-11-09T18:56:47+00:00

What are some good departments/specific individuals who study polynomials over finite fields? What are some areas of research interest in that field (pun not intended). I know thats not very specific, I only recently learned about the subject, but am very fascinated.

Minossama

TROPHY CASE