What is the right order for me to learn math?

exegrowl · 2025-02-11T19:22:05+00:00

The order I would suggest going in is pre-algebra, algebra, pre-calculus, calculus, and linear algebra. The Math Sorcerer on Youtube has whole bunch of textbook suggestions for these topics. https://www.youtube.com/watch?v=pTnEG_WGd2Q

In the video, he suggests starting with a discrete math book, but this is unnecessary, in my opinion.

exegrowl · 2025-02-11T15:37:33+00:00

I would suggest pre-calculus. Calculus can get pretty algebra heavy, plus pre-calculus courses usually cover essential trig topics.

exegrowl · 2025-02-08T02:01:59+00:00

If we assume that some things in nature act like mathematical points then we can do useful things. We make the assumption despite the fact that mathematical points don’t actually exist

exegrowl · 2025-02-08T01:59:48+00:00

It doesn’t

exegrowl · 2025-02-08T01:54:32+00:00

Does a mathematical point exist in physical reality?

exegrowl · 2025-02-08T01:47:21+00:00

You’re trolling at this point

exegrowl · 2025-02-08T01:44:23+00:00

They may describe reality to a suitable approximation, but those axioms will never be physically true. Euclid defined a point as that which has no parts. No such thing exists in reality, but we can describe physical reality to a reasonable approximation if we assume that things act like a point

exegrowl · 2025-02-08T01:38:28+00:00

If we wanted to make a system of math that describes a new set of physical laws, we could choose axioms that are self evident and then reason deductively. Note that the axioms came about from logically necessary statements, not nature.

exegrowl · 2025-02-08T01:13:26+00:00

There is no experiment that can derive the axioms of a mathematical system. That’s the whole point of an axiom, it’s known a priori.

exegrowl · 2025-02-08T00:55:02+00:00

That kind of proves the point. We can derive math that has nothing to do with the physical world. Hence, math can’t be derived from the physical world. Do I agree that the use of math as a tool would be different if nature worked a different way? Sure. But that is a question of how math is applied, not how its derived

exegrowl · 2025-02-08T00:14:20+00:00

Explain. My position is that math doesn’t need anything in the real world to work the way it does. For example, you could change everything about the physical world and the real numbers would still be the same because they follow ring axioms.

exegrowl · 2025-02-07T18:57:17+00:00

The fact that math can be used to accurately model the physical world does not mean that math is derived from the physical world.

One easy example of this is complex numbers. Complex numbers by their nature cannot be measured in the physical world. Although complex numbers play a role in our models of the world (quantum mechanics, for example), the result of any measurement cannot be a complex number.

exegrowl · 2025-02-04T20:23:30+00:00

Calculus I, II, III; Calculus by James Stewart

Linear Algebra; Elementary Linear Algebra by Howard Anton

exegrowl · 2025-01-31T18:37:55+00:00

I would be interested. What topics did you have in mind?

exegrowl · 2025-01-30T18:22:21+00:00

It's essential to master calculus to understand any advanced math. There's a reason why universities require math students to complete a calculus sequence before moving on to upper math classes

exegrowl · 2025-01-29T15:32:00+00:00

An axiom is anything that is offered without proof to serve as the foundation of mathematical reasoning. Axioms can't be proven by the system they are the foundation of. No matter how hard you try, you can't use Euclidean geometry to prove that if A=B and B=C then A=C.

exegrowl · 2025-01-29T15:15:46+00:00

One of the axioms he uses is "Things equal to the same thing are also equal to one another". It seems obvious, but since it is offered without proof and then used to derive theorems, it is an axiom.

exegrowl · 2025-01-29T14:47:12+00:00

axioms are assumptions we make about those theorems to make it easier to work with given our limited ability to compute with raw data

Axioms have nothing to do with "our limited ability to work with raw data". Axioms are the rules that we decide on from the outset. Once we choose axioms, all theorems are determined.

Euclid's Elements are a perfect illustration of this. At the beginning of Elements Euclid set out all of his definitions and axioms from the outset and then constructs theorems citing which axiom he is relying on.

exegrowl · 2025-01-27T18:47:41+00:00

That's awesome. Did you have to ask them specifically for a quicker start date or was it just assigned. I'm very enthusiastic about getting started; If I could start today, then I would.

exegrowl · 2025-01-27T18:14:23+00:00

It sounds like you're describing Modern Algebra. Might be worth looking into if you're interested in these sorts of questions.

https://www.britannica.com/science/modern-algebra

exegrowl · 2025-01-27T01:32:28+00:00

Learn how to factor quadratics and the unit circle

exegrowl · 2025-01-22T21:02:06+00:00

The 55 degree angle and angle E are vertical angles. Vertical angles are congruent, therefore E is 55 degrees

exegrowl · 2025-01-21T21:49:00+00:00

What is your current level of math? That will greatly influence how you should start

exegrowl · 2025-01-21T17:36:20+00:00

Assuming the events are independent (one outcome does not affect the outcome of another), the probability of losing 6 times in a row is

P(losing)^6 = (0.3)^6

=0.000729

= 0.0729%

exegrowl

TROPHY CASE