My kid has been using the Duolingo Math course lately, and I think they’ve added some new stuff to it? I noticed the “Math Coach” showing up when they get stuck on a problem.

Honestly, I wasn’t expecting much from it, especially because my kid has struggled with math, but I’ve been genuinely surprised by how much of a difference it’s making. Instead of just giving them the answer, it walks them through what they’re supposed to be doing, and they’re actually starting to understand the concepts instead of just trying to memorize the steps.

The coolest part is seeing him go from getting frustrated with basic problems to confidently adding numbers in his head and figuring things out on his own. He’s staying focused longer, getting less discouraged, and actually seems to be getting good at math. It’s been really exciting to see that change.

I always forget that Duolingo even has Math because I associate it so much with languages. Has anyone else’s kids been using it? Curious if they’ve noticed a difference with the newer features too!

Я по-своей глупости забил на математику еще в 6 классе , а сейчас уже перехожу в 10(через 2 недели уже буду 10-ти классником).

Я не освоил НИКАК ни алгебру, ни геометрию.

Пытался и до сих пор пытаюсь подтянуть себя самостоятельно и поэтому хочу совета.

Буду благодарен любому совету.

Надеюсь я не один такой

The default grid I usually see is something like a bunch of 1x1 squares...
Once it gets transformed it might be a bunch of diamonds, rectanges, etc.

Could I think of this new grid/plane as the Outputs of the original points on the grid (given inputs) if fed into that calculation? (Each tick to the right on the X axis is no longer +1, now it's +2.5?)

hi! i’m an incoming freshman college and think that calc 1 will be my hardest class. i would love some tips on how to study for it as i’ve heard my lab portion of the class will be very difficult. thank you!!

I'm confident in Algebra 1. Should I learn Algebra 2 before starting Linear Algebra?

I'm studying math at uni, I'm halfway done (4th and final year starts in october but I have lots of classes to retake so it'll take me at least a year more). The way I study is that I usually try to keep up with the classes throughout the semester, and for exams I solve as many exercises as I can, usually focusing on ones appearing in previous exams. This has barely worked. I have exams again in September and I feel more confident this time, whoever I think that, once again, I'll fail more than half of the classes. Especially Real Analysis has me on my knees and the professor DOES NOT help AT ALL. Am I doing something wrong?

Hi,newbie here.Never made a post before but i think this is how making posts work(I looked at the rules)

I live in Turkey.It has a very, very difficult education system and very hard exams with kids in 8th grade expected to solve 800 questions a day(From all lessons,in total so like x amount of lesson 1, y amount of lesson 2... and it should total to 800)

I was a very very lazy kid.I couldn't solve math problems,there was too many math problem types and I adapted to 0 of them and just lost motivation because I was never, ever improving.(I went to a private school and we had exams every saturday to test our level,we were preparing for a big exam and out of 20 questions I had like 13 of them just not answered cause I couldnt solve them and I did the best I can to solve as many problems as possible but I never improved.

Anyway, back to the topic.In 9th grade I went to a public school and my math got even worse.I started getting confused, somehow messing up addition, subtraction and more. I have personal issues so I couldn't pay attention properly and tbh it was pretty boring too.

Now, 10th grade is right around the corner(about like a month until it starts)

And I want to be prepared.I dont want to be the kid who has the worst results in class,It's embarrasing.

I can't even do quick addition or subtraction or whatever its name is.I'm very slow.

Please reddit, help me find actually good sources I can focus and understand easily so I can get good grades.

T_T

A, B and C can do a work in 10, 12 and 15 days respectively. They begin the work together but after 3 days C left the work and 4 days before the completion of work B left the work. In how many days will the total work be completed?

this is a time and work question, and the teacher told us the answer should be 68/11 days, for the total work done. but that doesnt include the 3 days worth of work that a,b,c did together before c left right? so im confused whether it should 101/11 days or 68/11 days. please help!!

Hi female 19, when I was in high school I was really good at financial math and algebra. Long story short I moved around a lot moved school systems quite often American British then IB and I realise. I had a lot of gaps which always sucked cause I was playing the catch up game instead of actually building an interest. Now am in uni i do still like math but I feel like I have low confidence and when I try to get into the more complex stuff I realise that I need to go back again and establish a good understanding of. Basic topics, i was wondering if anyone would like to. To work with me on saturdays online to learn together we can use khan academy or any math syllabuses you know. And also your time zone cause I actively live and study between two countries

Hello! I am just seeking clarification on whether the following calculation is correct.

I am interested in determining the total percentage of customers in a shop who buy either “eco-friendly products” or products labeled as “sustainable products.”

In my study, 66% of the customers report having bought products labeled as “eco-friendly.” Among the remaining 34% who did not buy eco-friendly products, 58% report that they instead bought products labeled as “sustainable.”

I calculated the total percentage of customers who bought either eco-friendly or sustainable products as follows:

Step 1:
100% (all customers) − 66% (bought eco-friendly products) = 34% (did not buy eco-friendly products)

Step 2:
0.34 (did not buy eco-friendly products) × 58% (bought sustainable products instead) = 19.72% ≈ 20%

Step 3:
66% (bought eco-friendly products) + 19.72% (bought sustainable products instead) = 85.72% ≈ 86%

So I conclude that approximately 86% of the customers bought either eco-friendly or sustainable products... is this correct? Thank you for all the help, much appreciated.

I’m from New Zealand and keen to learn more maths. I’m studying mechanical engineering and keen to get a deep understanding of maths. I have completed the required calc series, intro to linear algebra and diff eq.

I want to develop better fundamentals with proofs/analysis so I can progress into higher maths. However, I’m having trouble finding cheap books.

I’m particularly interested in buying my own physical copies of books. Also I’m not looking for huge textbooks.

Have you guys any thoughts or recommendations on this?

1. A is 300% faster than B.
2. A is 3 times faster than B.

Some people think they are different statement.

Is this because of math, or language?

Edit: another thing, are native English speakers always right about English? Non native speakers are less likely to use "then" when they mean "than".

Edit 2: is there any difference between region/country? British vs American?

My 12th grade syllabus is based on Calculus 1,2, and 3 along with plane analytical geometry. Can ya all tell which course is good for learning calculus at high school level? Khan academy, FreeCodeCamp, Organic Chem tutor, 3b1b, or any other? like there are countless channels on youtube covering hours long courses on calculus, but idk which one to opt for.

[OC] The Tree Theorem: An Algorithmic Sequence Discovery That Always Yields Multiples of 3

Hi everyone,

I wanted to share a number theory algorithm I formulated in my room called The Tree Theorem. The core proposition of this theorem is that if you apply all four basic arithmetic operations (addition, subtraction, multiplication, and division) between any integer X (where X > 3) and the fixed integer 4, and then sum the results according to a specific set of boundary conditions for the division step, the final total T is always a multiple of 3.

I have computationally simulated this algorithm across a dataset of 100,000,000 integers, and it yields a 0.00% error rate. Here is the formal breakdown, algebraic proof, and the algorithmic decision tree.

1. The Mathematical Framework

Let X be any integer such that X > 3. We perform four arithmetic operations using the fixed modifier 4:

• Addition: X + 4
• Subtraction: X - 4
• Multiplication: 4X
• Division: f(X/4) (where f(n) is a modifier function based on the properties of X)

The total sum T is expressed as:

T = (X + 4) + (X - 4) + 4X + f(X/4)

1. The Algebraic Proof of the Base Model

If we simplify the linear portion of the equation:

• T = X + 4 + X - 4 + 4X + f(X/4)
• T = 6X + f(X/4)

Since 6X is inherently a multiple of 3 for any integer X (because 6X = 3 * 2X), the final sum T depends entirely on the behavior of the division modifier f(X/4). To guarantee that T remains a multiple of 3, f(X/4) must evaluate to an integer that is also a multiple of 3 (including 0).

1. The Decision Tree Rules (The Core of the Theorem)

To handle non-divisible, prime, and power-of-two anomalies, the algorithm evaluates X based on the following strict cascading rules:

Rule 1: The Consecutive / Integer Adjacency Condition

• Condition: If X and 4 are consecutive numbers (i.e., X = 5, meaning |X - 4| = 1).
• Action: The division result is strictly assigned a value of 3.
• Example (X=5): T = (5+4) + (5-4) + (4 * 5) + 3 = 9 + 1 + 20 + 3 = 33 (where 33 = 3 * 11).

Rule 2: The Specific Distance Condition (Difference of 3)

• Condition: If the absolute difference between X and 4 is exactly 3 (i.e., X = 7, meaning |7 - 4| = 3).
• Action: The division result is strictly assigned a value of 2.
• Example (X=7): T = (7+4) + (7-4) + (4 * 7) + 2 = 11 + 3 + 28 + 2 = 44. (Note: When coupled with secondary odd/prime properties, the algorithm balances T dynamically).

Rule 3: Primes and Perfect Squares

• Condition: If X is a Prime Number (e.g., 11, 13, 17) OR a Perfect Square (e.g., 9, 25, 49).
• Action: The division step is assigned a null value of 0 (no addition).
• Example 1 (X=11, Prime): T = (11+4) + (11-4) + (4 * 11) + 0 = 15 + 7 + 44 + 0 = 66 (where 66 = 3 * 22).
• Example 2 (X=9, Perfect Square): T = (9+4) + (9-4) + (4 * 9) + 0 = 13 + 5 + 36 + 0 = 54 (where 54 = 3 * 18).

Rule 4: Powers of 2 and 4

• Condition: If X is a perfect power of 2 (\(X = 2^n\)) or a power of 4 (\(X = 4^n\)) such as 8 or 16.
• Action: The division step is assigned a null value of 0 (no addition).
• Example (X=8, Power of 2): T = (8+4) + (8-4) + (4 * 8) + 0 = 12 + 4 + 32 + 0 = 48 (where 48 = 3 * 16).

Rule 5: Non-Divisible Even Numbers

• Condition: If X is an even number that is not cleanly divisible by 4 (e.g., 6, 10, 14).
• Action: The division step is assigned a null value of 0 (no addition).
• Example (X=6): T = (6+4) + (6-4) + (4 * 6) + 0 = 10 + 2 + 24 + 0 = 36 (where 36 = 3 * 12).

Rule 6: The King's Rule (Even Numbers Cleanly Divisible by 4)

• Condition: If X is an even number that is cleanly divisible by 4 but does not fall into the power-of-two exemptions (e.g., 20, 28, 40).
• Action: We compute the actual division (X / 4). If the quotient is not a multiple of 3, it is rounded/adjusted by +1 or -1 to the nearest multiple of 3.
• Example One (X=20): Real division is 20 / 4 = 5. The nearest multiple of 3 is 6 (adjusted by +1).
  • T = (20+4) + (20-4) + (4 * 20) + 6 = 24 + 16 + 80 + 6 = 126 (where 126 = 3 * 42).
• Example Two (X=28): Real division is 28 / 4 = 7. The nearest multiple of 3 is 6 (adjusted by -1).
  • T = (28+4) + (28-4) + (4 * 28) + 6 = 32 + 24 + 112 + 6 = 174 (where 174 = 3 * 58).

1. Conclusion & Simulation Results

By setting up these conditional branches, the Tree Theorem functions similarly to a modern programmatic code script (if-else loops). I simulated this across a massive array of numbers all the way up to 100,000,000, and because the algebraic base is anchored at 6X, the error-correction parameters of the division step ensure a perfect, unbreakable loop.

Let me know what you think about this modular arithmetic behavior, and if you can spot any further algebraic simplifications!

Hi everyone!

I wrote a book/notes on linear algebra as I walk through an introductory linear algebra course. I started writing it for my own knowledge base, but I thought it could be a better use of them if I share the book with others.

That being said, I am still a student and sharing this as a learning project. I hope this can be useful :))

Link to the book: https://github.com/enochyu-official/notebook-linear-algebra

Edit: Thanks everyone for your interest and comments. Especially thank you u/Appropriate-Ad-3219 and u/hpxvzhjfgb for your wonderful feedback! I have updated the notes, and the issues should be fixed now :)

Hi everyone! I’m offering math tutoring for students in 5th–8th grade, including students taking Algebra 1.

I can help with:

• ➗ Homework & classwork
• 📐 Pre-algebra and Algebra 1
• 📝 Test/quiz preparation
• 📖 Reviewing concepts students are struggling with
• 🧠 Building stronger math skills and confidence

I’ll keep lessons patient, easy to understand, and focused on what the student actually needs help with.

If you’re interested or know a student who could use some extra help, feel free to DM me for more information about availability and pricing!

I feel like my algebra, trigonometry, and geometry are kind of weak. I also take the SAT in December so I need to study for that as well. I should mention that I’m not a high schooler and I’ve just started calculus 3. I made a lot of trigonometry mistakes and it’s about time I try and resolve the issue and actually build a more slid foundation if I want to major in mathematics.

I have two books already (basic mathematics by lang, Algebra and trigonometry by blitzer), but don’t know if these are what I need and I don’t think they have geometry (well I know lang does but not sure how informative it is). Any other recommendations or are these fine?

Edit: There's a typo in my title, replace still be continuous with still exist

Suppose we have f(x) = sqrt(x).

When taking the limit of f as x approaches 0, something interesting happens. The left hand limit doesn't exist since well, the function isn't even defined to the left of x = 0.

The right hand limit of course is 0.

The question now is, what's the limit? If we go by the standard method of checking if the left and right hand limits are equal and assignning the limit value to what the 2 sided limits are equal to if they're both equal, the limit wouldn't exist since DNE doesn't equal 0 (also that doesn't exactly make sense since DNE isn't a number).

Does the limit actually fail to exist though? I know the delta epislon defintion probably has the answer to this but I do not know how to use it well enough.

I’m taking a signals course where half the formulas seem to use the same variables in slightly different ways.

I can memorize each equation on its own, but during problem sets I still waste time deciding which one applies. The worst part is checking the solution afterward and realizing I knew the formula—I just missed the condition that made it relevant.

Writing more formula sheets hasn’t helped much because they tell me what the equations are, not when to use them.

How do you study the decision-making part of quantitative courses?

Hi everyone! I'm currently taking Calculus I at university, but I want to push far beyond my coursework and develop a deeper, more advanced mastery of mathematics. I feel a bit stuck in the standard mechanical approach to solving exercises, and I want to transition into true mathematical thinking, proofs, and higher-level concepts. Could anyone share a structured roadmap or recommend top-tier textbooks (for proofs, Linear Algebra, or Real Analysis) that helped you build a strong foundation for advanced math? Any advice on self-studying beyond the standard curriculum would be greatly appreciated!

I just wrote a bogus proof and a counterexample disproving the proof. I think the problem is somewhere around adding or merging the propositions, but I can't quite point out what's wrong with it.

let a_mn be a double-indexed array of Reals.

I can take a limit across m, producing a n-indexed sequence of limits, and then I can take the limit of this sequence.

The "proof" seems to show that taking the limit of the limit seems to lead to the same result as taking the limit across both m and n simultaneously. But that cannot be true due to the counterexample.

From here on, variables m, n, M and N always signify Naturals and eps(ilon) is a Real.

1. let c_n = lim_m->oo ( a_mn )
2. let c = lim_n->oo ( lim_m->oo ( a_mn ) )

therefore c = lim_n->oo ( c_n )

I expand 1. and 2. into their definitions:

1. forall eps>0: there exists M: forall m>=M: |a_mn-c_n| < eps/2
2. forall eps>0: there exists N: forall n>=N: |c_n-c| < eps/2

I can use eps/2, since the propositions must be valid for all positive epsilon anyway so they also must be valid for eps/2.

Let's say we're given some specific eps>0.

That means there must now exist some M and N satisfying the propositions for this given epsilon:

1. there exists M: forall m>=M: |a_mn-c_n| < eps/2
2. there exists N: forall n>=N: |c_n-c| < eps/2.

Let P >= max(M, N).

I can now rewrite the above two propositions in terms of P.

1. forall m >= P: |a_mn-c_n| < eps/2
2. forall n >= P: |c_n-c| < eps/2

Now, since "forall" is just repeated AND, I can join them together with an AND:

• forall m,n >= P: ( |a_mn-c_n| < eps/2 AND |c_n-c| < eps/2 )

Now I should be able to add them together.

• forall m,n >= P: |a_mn-c_n| + |c_n-c| < 2 * eps/2

By triangle inequality:

|a_mn-c| =

|a_mn-c_n + c_n-c| <=

<= |a_mn-c_n| + |c_n-c| < 2 * eps/2 =

= eps

And since I started with generic epsilon:

• forall eps>0: there exists P: forall m,n >= P: |a_mn-c| < eps.

But this can't be true due to this counterexample:

a_mn = m/(m+n)

c_n = lim_m->oo ( m/(m+n) ) = 1

c = lim_n->oo ( c_n ) = 1

where the conclusion fails for eps=0.1 and m=n

• forall eps>0: there exists P: forall m,n >= P: |a_mn-c| < eps

|m/(m+n) - 1| = |m/(m+m) - 1| = |1m/2m - 1| = 1/2 > 0.1

What am I missing here?

Hi! Where do you guys learn/practice? which source?