110.1K
BSSome continuous distributions. #math #manim #statistics #probability #datascience #bridgewaterstateuniversity
@bsumathdept
#Continuous Vs Discrete Variable
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PEReviewing some fundamentals across probability and random variables today 📚
References and resources:
- Deisenroth at al, “Mathematics for Machine Learning”, 2020
- Casella and Berger, “Statistical Inferences”, 2nd ed., 2002
- CM Biship, “Pattern Recognition and Machine Learning”, 2006
- “Lecture 12: Discrete vs. Continuous, the Uniform | Statistics 110” on Harvard University’s YouTube channel
- The course I’m following: “Mathematics for Machine Learning” by MathAcademy
@petal.byte
460.7K
MA✨️Code link in bio✨️In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = 1/√(2πσ²) e^(-(x-μ)²/(2σ²)) 📐
The parameter μ (mu) is the mean or expectation of the distribution (and also its median and mode), while the parameter σ² is the variance. The standard deviation of the distribution is σ (sigma). A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. 📊
Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal. ⚡
Moreover, Gaussian distributions have some unique properties that are valuable in analytic studies. For instance, any linear combination of a fixed collection of independent normal deviates is a normal deviate. Many results and methods, such as propagation of uncertainty and least squares parameter fitting, can be derived analytically in explicit form when the relevant variables are normally distributed. 🎯
A normal distribution is sometimes informally called a bell curve in data science and machine learning. However, many other distributions are bell-shaped (such as the Cauchy, Student's t, and logistic distributions). This demonstration shows the fundamental principles of probability theory that underpin artificial intelligence and statistical modeling. 🌟
#math #mathematics #fyp
@mathematisa
14.7K
COWhat they don’t tell you about Discrete math is that it can actually be really interesting and kind of fun IF you have the right resources and teachers!
I’m not gonna lie, the first time I took Discrete I failed!
Yes, it was the one and only class I have ever failed and it really sucked to get through an entire class only to get a failing grade!
I didn’t understand what I was doing wrong because I had really enjoyed the material at the beginning of the class but I just wasn’t able to keep up with the pace!
The second time I took Discrete, I focused my time on finding the best resources so that I could spend less time studying and more time applying the concepts!
These YouTube playlists helped me SO MUCH! They are all great teachers on the subject and each video gets right to the point so you can get a clear understanding of the material!
Are you taking discrete math soon?? Let me know any other questions you have about the subject and I’ll try to answer them in the comments!
Don’t forget to LIKE this video for more!
FOLLOW for computer science resources and motivation!!
#computerscience #computersciencemajor #computersciencestudent #discretemath #mathproblems #mathstudent #engineeringstudent
@compskyy
21.8K
THComplex variables
@therealmathsorcerer
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TH📈 Extrema of a Function: Peaks & Valleys! ⛰️✨
• Extrema are the highest and lowest points of a function—its maximums and minimums. They’re where curves reach their peaks or dips! 🎯
• Why it’s awesome:
Finding extrema helps us optimize—whether it’s max profit, min cost, or best design. ⚡
• Where it’s used:
💸 Economics – Maximizing revenue & minimizing risk
🌍 Engineering – Strongest structures with least material
🔬 Physics – Energy minimization in natural systems
🧠 Math – Optimization & calculus fundamentals
#mathematics #physics #animation #derivatives #calculus #geometry #functions #algebra #fyp #likeme #views
@the_mathsensei
223.2K
EQ➡️ Day-90/500 of Visual Interpretations of Mathematics: 🇮🇳 🌟
➡️ Experience India's 1st-ever visualization of differentiation as a limit! Witness the fundamental derivation come to life with unparalleled clarity and understanding. See how the concept unfolds visually, making it simpler than ever to grasp. Unlock a whole new perspective on differentiation! 🚀📈
➡️ Follow @equationacademy for more
#jee #equationacademy #math #edupreneur #animation #technology #mathematics#physics
#python #pythonprogramming#viralvideos #viralreels #trendingreels #trending #differentiation#calculus#exponential#limit
@equationacademy
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MA✨️video’s Manim code Link in bio- easy, fully explained & customizable.
Differentiation Made Simple! ✨️
In mathematics, differentiation is the process of finding the derivative of a function — the measure of how fast something changes. 🚀 It’s the foundation of calculus, showing us the instantaneous rate of change and the slope of a curve at a point. From velocity in physics to growth rates in economics, differentiation is everywhere. 🌍
👉 Why it matters:
✅ Understand how curves behave at every point.
✅ Learn why derivatives = slopes of tangents.
✅ See how the limit definition connects secant lines to tangents.
✅ Build stronger intuition for solving real-world problems.
🌟 Whether you’re studying for AP Calculus (US), A-Level Maths (UK), IB Math, or university-level engineering & science courses, mastering differentiation will unlock higher-level math and problem-solving. Perfect for exam prep, competitive exams, and self-study.
💡 Differentiation is not just for exams — it’s the language of physics, engineering, computer science, data science, economics, and AI. Once you understand it, you see change everywhere!
🚀 If you’ve ever wondered “how fast is this changing right now?” — that’s differentiation in action.
#differentiation #calculus #learnmath #fyp #views #likeme #explore
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@mathematisa
36.2K
VILet’s generalize
Time to formulate the Principle of Least Action and derive Euler-Lagrange equations in covariant form
1) Covariant means that under Lorentz transformations we must obtain the same motion equations
2) In this generalized approach the generalized coordinates and velocities are field potential and its derivatives correspondingly
3) This variational form can be used for any field be it:
s=0 - scalar particle - meson - strong interactions
s=1 - vector - photon - electromagnetic
s=2 - tensor - graviton - gravitation
s stands for spin
4) I am going to use the generalized Stoke’s theorem for hypervolume and hypersurface
5) From classical mechanics (previous reel on this topic) to electrodynamics, instead of Lagrangian we will use the Lagrangian density
6) This action S is represented in a form of 4-dimensional integral over the invariant 4-volume. Now we set its variation to zero: δS=0
7) Using the product differentiation rule, we obtain two terms. But according to the Stoke’s theorem and taking into consideration that the variation of q vanishes at the boundaries δq|_Σ = 0
8) Yay! Now we obtain generalized or covariant form of Euler-Lagrange equations.
Almost forgot: for this Landau II or IV
#womeninscience #womeninstem #quantumphysicist #theoreticalphysics #theoreticalphysicist #covariant #classicalmechanics #phd #phothesis #electrodynamics #quantummechanics #quantumphysics #quantumelectrodynamics #physics #science #girlinscience #quantumfieldtheory #cosmology #gravitation #vquantpost
@victoriaporozova
97.9K
THWhen Calculus Finally "Clicks" 🧠✨
Ever wondered what a derivative actually looks like? Stop scrolling and watch the magic of mathematics unfold! 📐
In this visualization, we’re looking at the function f(x) = \frac{1}{3}x^3 (the red curve) and its derivative f'(x) = x^2 (the blue curve). Watch how the slope value of the tangent line on the red curve perfectly matches the y-value of the blue curve at every single point. 🤯
Calculus isn't just about memorizing formulas; it’s about understanding the language of change. Whether you’re a math whiz or someone who struggled through high school algebra, there’s no denying the satisfying symmetry of a perfectly plotted derivative.
Why this matters:
Visual Learning: Seeing the slope translate into a new graph makes the Power Rule actually make sense.
Satisfying Aesthetics: The way the tangent line glides across the curve is pure brain candy.
STEM Inspiration: This is why we love science and math—the hidden patterns of the universe!
Tag a friend who needs to see this before their next exam! 👇Viral Hashtags
#Calculus #MathIsBeautiful #STEM #Education #MathVisuals Physics Engineering StudyGram DataScience Satisfying LearningMadeEasy Mathematics Derivative AhaMoment
@themathsmatriix
43.7K
ME🔹 Negative Determinant in 3D
In linear algebra, a linear transformation f: V → V between vector spaces can be represented by a matrix once we fix an input basis B1 and an output basis B2.
The notation M(f, B1, B2) denotes the matrix of f with respect to these bases.
How is it built?
Take each vector of the input basis B1 = {v1, v2, v3}.
Compute its image: f(v1), f(v2), f(v3).
Express each image in coordinates with respect to the output basis B2.
Place these coordinate vectors as the columns of the matrix.
So M(f, B1, B2) encodes, column by column, the coordinates of the images of the basis vectors of B1.
If we use the same basis for both input and output (for example, the canonical basis B of R³), then M(f, B, B) directly tells us the transformed vectors in the same coordinate system.
In the example we are visualizing:
The vector e1 (the x-axis unit vector) remains unchanged.
The vector e3 (the z-axis unit vector) also remains unchanged.
The vector e2 (the y-axis unit vector) flips direction: from (0,1,0) to (0,−1,0).
This creates a very typical situation:
The parallelepiped generated by {f(e1), f(e2), f(e3)} has the same volume as that generated by {e1, e2, e3}.
But the orientation changes: the cyclic order of the vectors no longer follows the right-hand rule, but instead the left-hand rule.
👉 The determinant captures exactly this:
If det > 0, the orientation of the basis is preserved.
If det < 0, the orientation is reversed.
In this case, det(M(f,B,B)) < 0, which tells us the transformation preserves volume but flips orientation, just like a reflection in a mirror.
#math #maths #physics #merlinomath
@merlinomaths
4.2K
INNormal Distribution - Your Probability Shortcut
Most natural and human-made processes follow the bell curve: symmetric, centered at the mean (μ), with spread measured by the standard deviation (σ).
Thanks to the 68–95–99.7 rule, you can predict where most values lie and make quick estimates without complex math.
Key Takeaways:
~68% of values lie within μ ± 1σ, ~95% within μ ± 2σ.
Standardizing with z‑scores lets you compare across units/scales.
The Central Limit Theorem explains why averages tend to look normal.
Tail risk? Beyond μ ± 2σ is only ~2.3% probability in one tail.
Why It Matters:
From exam scores to measurement noise, the normal distribution is everywhere.
Businesses use it to forecast demand variability, researchers to assess statistical significance, and engineers to control quality.
Knowing the shape, you can quickly gauge risk and probability.
Master this curve, and you'll read data like a native language.
Follow @insightforge.ai for daily, no‑fluff Data Science & AI tips.
#machinelearning #datascience #ai #education #technology #statistics #probability #centralLimitTheorem #math #analytics #viral #reels #fyp
@insightforge.ai
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