Data Science Decoded

Daily Math Academy Working towards mathematics for machine learning • First day back from vacation so was just getting back into the groove • Achieved 34/50 XP • Scored 11/14 XP on describing sets using Set-Builder notation • Scored 9/7 XP on defining vector valued functions • Scored 10/8 XP on the norm of a vector in n-dimensional Euclidean space • Scored 2/4 XP review on the “not” connective • Scored 2/4 XP on review on Gaussian elimination for NxM systems of equations

Daily Math Academy Working towards mathematics for machine learning • Achieved 52/50 XP • Completed lesson on Cartesian equation of a line 9/7 XP • Completed lesson on linear dependence and independence scoring 13/10 XP • Completed review on gaussian elimination for NxM systems of equations scoring 4/4XP • Completed lesson on the “not” connective scoring 9/7 XP • Completed review lesson on The Hadamard Product scoring 4/4 XP

Daily Math Academy Working towards mathematics for machine learning • Achieved 50/50 XP • Completed linear span of vectors in n-dimensional Euclidean space scoring 20/16 XP • Completed review on finding the inverse of a 3x3 matrix using row operations 4/4 XP • Completed review of further properties of determinants 6/4 XP • Completed review of parametric equations of a plane scoring 2/4 XP - there are some topics here I need to re-visit and couldn’t recall how to do • Completed quiz 1 scoring 18/15 XP

Daily Math Academy Working towards mathematics for machine learning • Achieved 48/50 XP • Completed lesson on introduction to abstract vector spaces scoring 9/10 XP • Completed lesson on the image of an affine transformation scoring 15/16 XP • I remember coming across affine transforms for the first time in a computer graphics class at university through a Java library but had never been introduced the topic at the time - I just saw it as a way to rotate or translate objects on the screen • Completed lesson on boolean functions scoring 18/14 XP • Completed review lesson on domain and range of quadratic functions scoring 6/4 XP

I can really relate to this recently when I’m starting hit my knowledge frontier of math and most of the lessons are no longer re-learning stuff I’d forgotten but actually new topics (I’ve an MEng in Electrical Engineering for context) The great thing about the math academy system is it guarantees you have the pre-requisite blocks in place before doing something new For example, differentiating inverse trig functions was something new to me but because I was solid on all the other diff. rules that come before it means that my entire focus for the lesson can be on ensuring I’m handling the inverse functions correctly I’m not wasting time thinking, ok how does the chain rule work again or this is a function times a function what’s the rule for that again? I remember back to electrical engineering undergrad where so many of the circuits classes took more time than necessary as I’d forgotten pieces of math that acted like weights around my ankles when trying to work through the material (e.g complex numbers, switching between polar and exponential forms etc etc) Learning new topics on the system almost feels “friction” free in terms of the only thing in the lesson I need to worry about is the new concept being taught and making sure I am getting that right

People often judge their potential through the lens of a poorly designed learning experience. One reason so many people underestimate what they can learn in math is that they have never experienced what it feels like to learn from a genuinely coherent prerequisite structure. Once the structure is repaired, the math often feels far more learnable than it did before.

Daily Math Academy Working towards mathematics for machine learning • Achieved 40/50 XP • This is the first day working on the upgraded mathematics for machine learning curriculum and all of the lessons were ML curriculum rather than foundations • Completed lesson on Gaussian elimination for NxM systems of equations scoring 15/12 XP • Completed lesson on the domain of a vector valued function 7/7 XP • Completed lesson on the parametric equations of a line scoring 9/7 XP • Completed lesson on truth tables scoring 9/7 XP

That diagram brings back memories I remember the first ML course I did about 8 years ago said don’t worry about the math just get intuition and focus on the libraries for the first part of the course to build projects Then about half way through just dumps this on a page, expects you to get it and carries on with using libraries for the rest of the course with little to no explanation where any of this comes from Was a real life genuine, draw the rest of the owl moment

Too many people think growing up is about putting the legos down and doing grown-up stuff instead. The real ones know that grown-up stuff is just legos with more complex bricks. You never had to put the legos down. You just needed to upgrade your set to use Jacobian matrices.

Daily Math Academy Working towards mathematics for machine learning • Achieved 32/50 XP • Most of my time today was spent on doing the diagnostic exam for the new version of the mathematics for machine learning course • My % completion has actually increased from ~ 11% to ~21% • Did one lesson on the “AND” and “OR” connectives scoring 6/7 XP • Will be back onto lessons from tomorrow and I can see the new lesson list is mostly now on mathematics for machine learning content • My completion status for MF II has now been upgraded to 95% and my completion status for MF III has been upgraded to 79%

@ninja_maths Good stuff, I've been on the M4ML track for about 9 months and just about to complete MF II and MF III so this is ideal timing for me personally

➕Major Additions Matrix Calculus: Vector & matrix derivatives, including total derivatives and gradients → Core for neural nets & backpropagation Multivariable Optimization: Critical points, second derivative tests, Lagrange multipliers → Essential background for Support Vector Machines and constrained optimization Logic & Boolean Algebra: Predicate logic, equivalence, Boolean functions → Explains model expressivity (e.g., why XOR requires a multi-layer neural network) Linear Algebra Enhancements Hadamard Product, and element-wise operations → Used throughout neural networks Distance Metrics: Euclidean, Manhattan, Minkowski → Foundation for k-nearest neighbors, clustering, and similarity Feature extraction using Principal Component Analysis: → Tied to SVD and high-dimensional data analysis 🔢 Foundations & Notation Stronger Set Theory + Optimization Language: Supremum/infimum, argmax/argmin, indicator functions with predicates → Matches how machine learning is actually written and taught 🎲 Probability & Statistics Added: The law of total expectation Removed: Hypothesis testing (less central in machine learning practice) Kept: Maximum likelihood estimation & confidence intervals

I'm happy to announce that we've just released a major update to our Mathematics for Machine Learning course! Here’s a summary of what's new.👇

Daily Math Academy Working towards mathematics for machine learning • Achieved 47/50 XP today • Completed describing properties of the secant function scoring 9/7 XP • Completed describing properties of the cotangent function scoring 9/7 XP • Completed Quiz 35 scoring 15/15 XP • Completed review of calculating the inverse of a 3x3 matrix using the cofactor method scoring 10/8 XP • Completed review of unit vectors scoring 4/4 XP • I’m now at 92% for math foundations II and 76% for math foundations III • Roughly estimating my completion means going through the foundations track will have taken me approx 1 year after being placed at MF II After that it will be purely mathematics for machine learning content first - and then all the other interesting courses that math academy has released!

Daily Math Academy Working towards mathematics for machine learning • Achieved 47/50 XP today • Completed describing properties of the secant function scoring 9/7 XP • Completed describing properties of the cotangent function scoring 9/7 XP • Completed Quiz 35 scoring 15/15 XP • Completed review of calculating the inverse of a 3x3 matrix using the cofactor method scoring 10/8 XP • Completed review of unit vectors scoring 4/4 XP • I’m now at 92% for math foundations II and 76% for math foundations III • Roughly estimating my completion means going through the foundations track will have taken me approx 1 year after being placed at MF II After that it will be purely mathematics for machine learning content first - and then all the other interesting courses that math academy has released!

Daily Math Academy Working towards mathematics for machine learning • Achieved 54/50 XP today • Today was one hell of an amount of trig lessons, 5 completed in total • Completed describing properties of the tangent function scoring 7/7 XP • Completed describing properties of the cosecant function scoring 9/7 XP • Completed combining graph transformations of tangent and cotangent scoring 9/9 XP • Completed limits of reciprocal trig functions scoring 14/11 XP • Completed graphing reflections of trig functions scoring 9/7 XP • Completed review lesson on conditions when a determinant equals zero scoring 6/4 XP

Daily Math Academy Working towards mathematics for machine learning • Achieved 48/50 XP today • Completed combining graph transformations of secant and cosecant scoring 14/15 XP • Completed further properties of determinants scoring 14/11 XP • Completed limits of trigonometric functions scoring 13/10 XP • Completed describing properties of the cosine function scoring 7/7 XP

Daily Math Academy Working towards mathematics for machine learning • Achieved 51/50 XP today which is the highest for a while and back hitting my daily XP target • Completed quiz 34 scoring 15/15 XP which I was happy with • Completed a review of hyperbolic functions although the review lesson didn’t contain the one I got wrong which was sinh rather than tanh • Completed lesson on conditions when a determinant is equal to 0 for 6/7 XP • Completed lesson on symmetric matrices for 7/7XP • Completed integration using inverse trig functions for 9/7XP • Completed review of vertical asymptotes of rational functions for 4/4 XP • Completed review of modelling with the Poisson distribution for 6/4 XP

Daily Math Academy Working towards mathematics for machine learning • Achieved 45/50 XP today • Completed lesson on elementary trigonometric equations containing cotangent scoring full marks of 18/18XP • Completed lesson on graph transformations of tangent and cotangent scoring 7/7 XP • Completed lesson on describing properties of sine function scoring 7/7 XP • Completed lesson on volume of parallelpipeds scoring 13/13 XP • Scored full marks on all lessons but no bonus points today • Good to start to the week completing this before work starts, I much prefer doing math academy in the morning when I’m fresh and sets me up well for the day

Daily Math Academy Working towards mathematics for machine learning • Achieved 44/50 XP today • Fifth day in a row and want to keep building momentum again to make progress • Completed lessons on vector projections, differentiating inverse reciprocal trig functions + powers of matrices • Scored full marks on all lessons but no bonus points today

@ninja_maths You guys are on a roll recently! Also I really enjoyed your appearance on the @_MathAcademy_ podcast with Justin and Jason. Good to hear perspectives from someone else from the UK

Mathematical Methods for the Physical Sciences (MMPS I & II) is a new, two-course curriculum built around the mathematical tools that physicists, engineers, and applied scientists actually use. The idea is simple: instead of learning math subjects in isolation (linear algebra, multivariable calculus, differential equations, probability), organize them into a coherent toolbox for modeling the physical world. You can think of it as a modern sequence on mathematical methods that shows how the pieces of applied mathematics actually connect. MMPS I builds the core mathematical language used across the sciences: • Linear algebra: matrices, determinants, vector spaces, eigenvalues, diagonalization • Multivariable calculus: gradients, Jacobians, vector fields, divergence, and curl • Multiple integrals and coordinate transformations • Probability and random variables (with Gaussian models and expectation) • First- and second-order differential equations • Physical modeling with ODEs (oscillators, circuits, growth/decay) Then, MMPS II builds the more advanced toolkit used in real scientific modeling: • Inner products, orthogonality, projections, Gram–Schmidt • Quadratic forms, spectral theorem, singular value decomposition • Least-squares and data fitting • Vector calculus theorems (Green, Stokes, divergence) • Surface and line integrals • Systems of differential equations and phase portraits • Laplace transforms • Boundary value problems and Fourier series • Numerical methods for differential equations • Multivariate probability and the central limit theorem In other words, MMPS II gets into the mathematics behind: – Vibrations and waves – Electromagnetism – Diffusion and heat equations – Dynamical systems – Signal analysis – Uncertainty propagation – Computational modeling Who might benefit? • Physics students • Engineering students • Applied mathematics majors • Computational science students • Anyone interested in modeling real physical systems And we’re not done yet. We’re also planning a third course in the near future that pushes deeper into the mathematics used in theoretical physics and advanced applied math. Topics we’re planning to include: • Partial differential equations and separation of variables • Special functions • Tensors • Functions of a complex variable • Group theory • Additional integral transforms • Calculus of variations • Perturbation methods In other words: the mathematics behind quantum mechanics, field theory, continuum mechanics, and modern mathematical physics.

I'm delighted to announce that @_MathAcademy_ has released two courses in Mathematical Methods for the Physical Sciences. Designed for students who want the mathematical tools needed for undergraduate-level study in physics, engineering, and other STEM fields. Details below👇

So I was today years old when I made the realisation that all the values for sine and cosine come from the unit circle after doing numerous @_MathAcademy_ questions on it I can’t quite believe I never made this connection before given that I’d done trigonometry, unit circle, trig equations and adjacent topics numerous times throughout high school and university

Daily Math Academy Working towards mathematics for machine learning • Achieved 48/50 XP today • Fourth day in a row and want to keep building momentum again to make progress • Completed lesson graphing the inverse tangent function as a result of failing review lesson and scored 7/7 XP • Did quiz 33 re-take and scored 18/15 XP, after the review I really felt my understanding and efficiency with inversing matrices has gone up a level • Completed 3 more review lessons • Completed 1 new lesson on combining graph transformations of sine and cosine scoring 11/11 XP