What are everyone's mathematics skills?

[jordan]

Hey, would someone in college (I know dave and bloodhound are) list the math-based clases they have taken so far and are planning to take? I just got a course book from a school that is semi-well-known for their math program and wanted to see how it stacked up to what you guys are taking.

[bloodhound]

For my first year I did te following modules:-

 

1)Foundation of Pure Mathematics:

>Combinatorial Counting

>Number Systems, Rationals and Irrationals

>Set and Relations

>Functions, Permutations and Countability

 

2)Mathematical Structures:

>Mappings, Permutations and Symmetries

>Groups

>Integer Arithmetic and Cyclic Groups

>Polynomials

>Metric Spaces

 

3)Analytical and Computational Foundations:

>Introduction to MAPLE

 

>The basic language of sets

>The logical statements

>Direct/Indirect proof, proof by contradiction/induction

>Inequalities

 

>Existance of the least upper bound

>Sequences

>Algebra of Limits, Sandwich theorem and monotone sequences

>Limits of Functions, Continuity

>Indeterminate forms, L'Hopitals Rule

>Iterative sequences, Contractions

>Newton-Raphson

>Improper Integrals

>Introduction to Series

>Tests for convergence

>Power series, Interval of Convergence

 

4)Linear Mathematics:

>Complex Numbers

>Vector Algebra and Geometry

>Matrix Algebra

>Linear Systems

>Eigenvalues and Eigen vectors

>Vector Spaces and Subspaces

>Spanning sets, Linear Independence and Bases

>Linear Transformations

>Rank and Nullity

>Rank of a Matrix

>Inner Product Spaces

>Norms

>Hermitian products and Unitary Spaces

>Gram-Schimdt Orthogonalisation Procedure

>Diagonalisation of Real Symmetric and Hermitian Matrices

>Quadratic Forms

 

5)Calculus:

>Functions of one variable

>Limits and Continuity

>Differentiation

>Theorems of Differentiation

>Stationary points of a function

>Integration

>Numerical Integration

>First order differential equations

>second order differential equations

>Laplace Transforms

>Functions of more than one variables

>Partial derivatives

>Taylor's Theorem for function of two variables

>Multiple integrals

 

Continued.....

[bloodhound]

6)Probability:

>Sample spaces and events

>Probability and counting problems

>Conditional probability and independence

>Random variables

>Expectation

>Standard discrete random variables

>Continuous distributions

>Transformations

>Sums of random variables

>Bivariate random variables

>Central limit theorem

 

7)Statistics:

>Exploratory Data Analysis

>Point Estimation and Data Analysis

>Hypothesis Testing

>Regression and Correlation

>Categorical Data Analysis

 

8)Modelling and Dynamics:

>Introduction to modelling: diversity of applications; models as descriptive and predictive tools; model classification; the modelling cycle; approximations; dimensions and units

 

First modelling examples: modelling populations with sequences

 

Kinematics: distance, speed and acceleration; integrating to determine motion; frames of reference; kinematics with vectors; relative velocity

 

Dynamics: motion of a point particle; Newton's laws; forces in equilibrium; resolving forces; static friction; particle motion in three dimensions; projectiles; inertial frames; conservation of momentum in collisions; energy for linear motion; angular momentum and moments; systems of particles, centre of mass; equilibria of rigid bodies.

 

Simple harmonic motion: damped and forced systems; resonance; potentials

 

Variable mass problems

 

Systems of nonlinear equations: linearisation; phase plane analysis

 

Two-dimensional motion: projectiles revisited; velocity and acceleration in polar coordinates; circular motion;

 

Introduction to special relativity: Lorentz transformation

[Dave]

You did a hell of a lot more than I did - on calculus, we just about crawled up to power series and Taylor expansions of one variable. But then again, we've proved bloody everything under the sun up until that point, so maybe we'll get going this year.

[MolecularMan14]

well, im going into non-euclidian geometry, and analytic geometry, both of which i never intend to use in my genetic career

[deltanova]

my strongest point is geometry,yet im still not realy good at maths (im only in intermediate) i think ill need to buck up on my algebra.

[pulkit]

my strongest point is geometry,yet im still not realy good at maths (im only in intermediate) i think ill need to buck up on my algebra.

 

You really come to know what maths truly is once you get out of school. You have a long long way to go.

[deltanova]

Yeah, a realy long way i can bet, ah well one step at a time.

[coquina]

I don't do well when it comes to "theoretical math" - I grew up in a machine shop reading blueprints and making parts. Machinists primarily need to know geometry and trig. You also use algebra to calculate the proper speeds and feeds - the two components of cutting tools - how fast the spindle turns and how fast you feed the tool into the part.

 

When the computer age dawned, I learned to program machine tools - based on and x,y,z coordinate system. In order to program the cutting tool, you start out by laying parallel lines around the part at a distance equal to the radius of the tool. If you have a contoured surface, "curves", you have to figure the tangent point of the tool where one curve ends and the next begins. I used to to this manually, and it was a royal PITA.

 

Now I use CAD/CAM. I draw the part I want to cut on a computer screen - draw the offset for the center of the tool, make sure all the lines are connected, select the direction and side of the tool, and the computer writes the program. I can write programs for complex parts in minutes that previously took days.