Results day is kinda....

(Wrote a little something after Year-1 ended :0 ... )

Results day is kinda like a double release - a break from the grind and seeing those numbers drop (and hopefully, pop). 2 hours ago, some pretty neat figures showed up on our screens, isn't it? Caught a glimpse of three, and I snapped them up before sleep takes over, but I wanted to write here anyway.

Just wrapped up Year-1, and it genuinely flew by! A time I will remember for what's worth, despite a small hiccup with a late penalty and two sub-criteria that scored less than needed to yield a distinction overall. Already sensed this. If things had fallen just right, I might have hit a distinction. Right after the assignment guidelines are released, get started on them. Work on the study material and the assignment "simultaneously." Don't "wait" to understand it all before beginning the assignment; it may not be as effective as you think. Even though we receive the official assessment documents and details, create your own file that breaks down the assignment into the level of detail you need. Expect to revise and update this file regularly, as the instructions provided can sometimes be erroneous or unclear. And if one ...flowchart can't be enough to bring a 90ish to a borderline distinction, I don't know what else will. Hmm.

All in all, I'm really pleased with how one extremely exhausting credit turned out...88%. Even in the first-ever, toughest, most demanding subject, where many were ahead of the show (their work in labs and etcetera was amazing), that 2 infinities were pleasing to the G.

Even though first term felt like a lot of work, longer than this term, not that it didn't pay off as much as it did now but this term has some solid credits and it felt like a sprint. Thus, I'd particularly remember this, also for the highest %s to date. Yes! The final exam wasn't a piece of cake but rather a collection of intriguing pieces, particularly the last 2. In hindsight, I couldn’t be more delighted to get a 92% overall in a credit that was heavy on problem-solving tasks and included this final exam. You either hit the jackpot or get hit by a jack.

You may miss the math already. Nostalgic …this means more than one thing. That they were actually better than the future stuff.

P.S. And another term passed...That turned true in the same Math credit itself. The last or maximum math credit with a poorly presented/formatted heavy-weightage paper on a hideous interface, which could barely show a single option in entirety (writing them on paper? knowing those robust equations that are as long as you can imagine?....yeah, no thanks. Checked the duration available?). So whatever 100s (and the rigor of it) you received so far can go sleep. Just Lose it.

Pro Tip (Year-2 exemplifies this) :

Overall, one can't be certain, only make educated guesses about whether things are looking better or worse. Even if you only have a few more before winding up, give that extra something a shot – just "try." That effort could contribute to about 5-10% of the overall picture. Prepared for leaving almost >20% (weighatge) of the story? And in hours closer to wrapping up the work, turned out you had a shot at 20% + _% (score) !

As for functions, (elementary) algebra, and trigonometry in college, these are naturally integrated into everything, i.e. by default. Linear algebra, Complex numbers, Statistics and Probability are the overarching topics, before Calculus hits in :

Trigonometry includes calculating functions in right-angled triangles, converting versions, and applying identities for angle sums, differences, and double angles. It also involves defining, verifying the existence of and computing inverse functions & solving trigonometric equations (linear, quadratic, and those requiring substitutions) and their inverses. Graphical and algebraic ways to establish relationships.

Understanding, identifying and solving functions like polynomial, rational, piecewise defined, root, power, even, odd, increasing, decreasing, exponential, and logarithmic functions. You’ll also learn how to derive new functions using BODMAS and composition.

Ways to represent Complex numbers, computing conjugates, De Moivre's theorem, finding roots of complex numbers, and complex roots of real quadratic polynomials.

Systems of linear equations, discussing definitions, classifications, solutions methods including Gaussian elimination, and matrix-related properties.

Matrix algebra, covering definitions, operations, transformations, and properties of matrices.

Specific types of matrices (augmented, symmetric, upper and lower triangular, block matrices, orthogonal matrices) and their properties, including recognizing these matrices and understanding their relevance

Composition of transformations (e.g., rotations with reflections), and the use of transformations in geometric contexts (e.g., defining rotations and reflections in R^2),

Detailed methods for computing determinants (e.g., cofactor expansion) and the specific application of determinants in solving systems (Cramer's rule) and polynomial interpolation

Linear transformation and determinants, emphasizing solving systems, defining transformations, and using determinant properties.

Eigenvalues, eigenvectors, and diagonalisation, with a focus on defining, calculating, and applying these concepts.

Vector geometry, defining and computing with vectors, understanding linear transformations, and applying cross products. Operations like finding the parametric equations of lines, computing the distance from a point to a line or plane, and recognizing orthogonality and parallelism

Probability, covering definitions, distributions, and rules for computing probabilities.

Bayesian probability, sampling methods and z-scores.

Distributions of random variables, focusing on understanding and applying various statistical distributions and specific rules (68%, 95%, 99.7% rule)

Only one math variant was wrapped up with some solid exam prep, which is my fave about it. It included hyperbolic functions, multivariate functions, and their operations, e.g., graphical representation using level curves and contours, differentiating multivariate functions using partial derivatives, multivariate chain rule, differentials, and linear approximation. You'll inherently encounter similar knowledge of functions and trigonometry from the previous version.

Now, it's just that you'll branch them out into limits, derivatives, differentiation, and integration and its applications like area, volume, power series, Taylor and Maclaurin series, and power series approximation. Perhaps add in some modulus, power, hyperbolic, and composition functions.

Figure out the shape of the graph, domain, codomain, range, derivatives, and integrals of each function you came across so far.

Also, don’t forget inverses and functions with restricted domains.

As for integration, study properties of integrals, antiderivatives, definite and indefinite integrals, the fundamental theorem of calculus, and using standard integrals and conversions to them.

Touched upon differential equations, integrating with partial fractions, separable first-order DEs, and linear first-order DEs.

Be careful while dealing with limits (I know it's for infinite and finite values, and it seems like you just plug in the values, but...wait until graphs hit), graphs and transformations, L'Hôpital's rule, logarithmic and implicit differentiation, and integration techniques (by parts, substitution, and any further techniques). For instance, I remember my first few days with this rule when I first heard of it. You have to deal with the function in front of you ‘separately’. You apply the rule to the numerator and denominator separately.

Review a variety of functions you’ve explored so far, as well as basics of derivatives, various rules to calculate derivatives of functions, partial derivatives and integrals. Starting from calculations of partial derivatives for functions with more than two variables to evaluating the integral of a function, it could feel like a good refresher. One quick mention: Try not to underestimate the logs part. Actually, work them out on paper without a doubt.

Get introduced to ODEs, classify them and explore simple approaches to solving them, particularly solving by inspection. Learn about the 4 systematic methods to analytically solve first order ODEs : separable form , form of dx/dt = f(x/t) {assuming x > 0 , t > 0 : you’ll get why}, the exact form and the linear differential form.

Numerical Solutions of First-Order ODEs are introduced, focusing on the Euler method and basic principles of numerical solutions. By now, a good variety of First-Order ODEs could have been explored.

Study the methods to solve Linear Constant Coefficient Second-order ODEs and their applications.

Call it a wrap with Laplace Transform and Its Application & Fourier Series Expansion.

And this wasn't it. Where's Stoke's Theorem? Double/triple integrals in polar, cylindrical and spherical coordinates? Vector Calculus?