/sci/ - Science & Math

>>6560733
this one?
>>6560160
scipy probably

What was the first theorem that you proved all by yourself? Which proof do your consider your best or most elegant?

Is the "set of all fields" a set?

How legit is this pic?

>>4831968
Learn
1) Vector Calculus
2) Intro to Proofs
2.1) Mathematical Logic or Metamathematics would help get experience with very abstract and gigantic fugly proofs that you will see later
3) Proof bases rigorous Linear Algebra
4) Abstract Algebra at the level of Artin
5) Real Analysis
6) Complex Analysis/Calculus
7) Partial Differential Equations and Fourier Analysis
8) Probability Theory
9) DIFFERENTIAL GEOMETRY (prepare your anus)

>1)Elementary Physics
Algebra and Trigonometry, maybe Geometry and some familiarity with Differential & Integral Calculus
>2) Intermediate
Vector and Multivariate Calculus, Ordinary Differential Equations, Partial Differential Equations, Complex Calculus, Probability Theory (both Continuous and Discrete), and Matrix Algebra. [Basic Statistics for lab work wouldn't hurt]
>3) Advanced
Linear Algebra, Abstract Algebra, Advance Group Theory, Group Representation Theory, Lie Algebra, Differential Geometry, Complex Analysis, and some Real Analysis.
Also you need to rapidly become aware of all special functions: Green's function, Bessel functions, etc...
>4)Quantum n' shit
Linear Algebra, Abstract Algebra, Advance Group Theory, Group Representation Theory, Complex Analysis, and some Real Analysis.

I'm curious...what kind of work is done in the field of theoretical computer science?

pic unrelated.

>>4404824
why yellow?

>>4100165
>You learn at least as much math as most physicists, but ultimately focus more on working with data and data-structures.

Oh? Can you name the classical Lie groups or define what a tensor is? Do you know the Laplacian?

>inb4 you imply physicist don't use/learn combinatorics/probability in statistical mechanics and QM...

Registering for classes soon and I 'm forced to choose one of following courses to take since they're both at the same time.

Intro to Differential Geometry: develops much of the language and many of the basic concepts of differential geometry in the simpler context of curves and surfaces in ordinary 3 dimensional Euclidean space. Builds both a solid mathematical understanding of the fundamental notions of differential geometry and sufficient visual and geometric intuition of the subject. After completing this course, the students will be in a position to (i) apply their knowledge and skills in this course to their related subjects, (ii) be ready to study more advanced topics such as global properties of curves and surfaces, geometry of abstract manifolds, tensor analysis, and general relativity.


Formal Languages and Automata: Provides a rigorous mathematical framework for two general areas: that of language description and that of computation; to examine the relation between the two and to consider practical applications from Computer Science and Linguistics. Computability theory and complexity theory are also introduced.
Topics:
Regular languages and automata
Context-free languages and Pushdown Automata
Turing Machines and Decidability
Hierarchies and properties of language families
Computational Complexity Theory

Has anyone taken any similar courses and would recommend it over the other?

You don't learn shit in pop science books (assuming your over 10 years old). Get a REAL textbook if you want to start to learn anything. Hearing of the wonders of physics/science is not learning of physics or science.

First buy a Vector Calculus Textbook
Then a Gen Chemistry - University Physics - Probability/Statistics - Linear Algebra textbooks
Then somewhere around here you're supposed to have already learn programming and the basics EE/CompE.
Then Ordinary&Partial Differential equations - Mathematical Proofs - Organic Chem Textbooks - Experimental Physics/Error analysis
Then whatever you want to learn at the INTRODUCTORY level: Electromagnetism/Quantum & Atomic Physics/Astrophysics/Thermodynamics & Statistical Mechanics/Classical Mechanics
Next pick what you want to learn.
Then more math: Real/Complex Analysis, Abstract Algebra, Differential Geometry, etc in whatever you need to know to go farther in you chosen direction.
Finally get graduate textbooks and start reading published research papers

Then you might get a sense of real understanding of a SMALL aspect of science. Also somewhere along the way you would have gotten a BS/Master/PhD, usually... Then you learn the horrors of the Tenure track and peer reviewing and question why the fuck didn't you major in political science.

all of this

>Explain calculus, why it matters, and what it's actually useful for.

Back in WWII, schools couldn't teach Real Analysis fast enough to Engineers; so they remove any thought involved in the subject and created calculus.

And yet people still fail in droves. Unless you go into the soft sciences where calculus is the heavy artillery, it is the shit you do AFTER you solved something to get concise answer.

>>3336710
>calculus
>serious physics

nope, see pic for maths used in physics

>>2333793
Bullshit, Physics maybe but not CS.

Is there any kind of University League Table for postgraduate degrees?

ancient BAMP

Is it true that ALL non-invertible matrices have liner equations that, when plotted, lay on the same line?

picture is delicious

I'm studying Mathematics in university, and we're going to have to start choosing the topic for our Final Year Project.

>You should choose a topic that interests you and that allows you to demonstrate your independent research skills. Topics that are already well treated in textbooks or popular articles may make it difficult for you to do something original or to demonstrate your skills in researching information yourself. A successful project on such a topic would need to demonstrate your powers of analysis and presentation of the material.

I've been trying to think of something to do; initially, I was considering the 3D Mandelbrot Set as a topic, but in order to compute this, I'd have to do thousands of calculations, and I have nowhere near the computational power needed at my disposal.

Do you guys have any suggestions for interesting topics that aren't already well treated?