Pawan > Recent Status Updates

Since Euclidean Geometry is deeply ingrained, adopting a new form of geometry becomes difficult, and feels slow. Metrics seem equivalent to distances, and they are computed using metric tensors which are, in essence (I understand), transformation matrices on Reinmann geometry over manifolds.

My practical excursions equate metric tensors to weights in learning algorithms. I need to watch some lectures.

Ex-Wife is supposed to be fired from the exosphere to be effective as a KKV. Justin Hammer didn't sell defective product - Colonel Rhodes didn't read the manual.

Problems without reference to reality can feel bland, so:

1.13 (terminal homing), 1.33 (pre-impact destruct), 1.45 (rifle), 1.59, 1.84 (g-force), 1.89 (cycling on hemisphere), 1.100, 1.101, 1.104, 1.111 (aim adjustment), 1.130 (F is downward), 1.136 (hotwh

Too long - and that's without considering the plentiful short-forms.

Appendix F (and exercise 5.22) were beyond me. F.5, F.23, F.27, F.34 (of those that I did try), G.3, G.5 to G.11 (FORTRAN).

3.7, 3.8, 3.11, 3.12, 3.14, 3.15, 3.17, 4.1, 4.5, 4.6, 4.11, 4.12, 4.14, 4.17, 5.2, 5.8, 5.9, 5.12, 5.15, 5.16, 5.18, 5.19, 5.28 (map and reduce).

WSC is a far cry for someone who wishes for a workstation. Most of the exerci

I hope to apply all I have learnt. It's a bit much:

A.6, A.7, A.8, A.12, A.13, A.14 to A.18, A.20, A.22, B.4, B.6, B.13, B.15, C.5, most of those in appendix D (and they are by the authors of an operating systems book).

1.3, 1.6 (why not blow up and out like in the mission impossible ghost protocol movie), 1.7, 1.9, 1.11, 1.15, 2.3, 2.5, 2.15, 2.16, 2.19, 2.23, 2.30, 2.34, 2.35, 2.38, 2.40, 2.43, 2.44, 2.45, 2.47,

Most of the exercises are numerically intensive (non calculus based) formula substitution arithmetic for averages, expected values and more using tables and charts. I might want to share some interesting ones.

I had read a chapter on charged coupled devices from a semiconductor physics book which also discussed other transistor level fabrication intricacies (that I will read some other time). Ironically, books that

Miscellaneous problems are entertaining, 105 being the most fun. Problem 106 can also be solved with postulates of group theory or graph theory, I think.

I will retry all the problems at a much later date, especially the ones I couldn't solve. There are 65 odd problems in Appendix A which are for a proper time test.

Problem 43 likely has a print error, and problem 92 asks for unordered set pairs.

I was excited about combinatorics because I wanted to try counting on a soroban. Of the problems that are application of Pigeon Hole Principle (79, 81, . . ., 98), my favourite was 86 because it combines trigonometry in a clever way. Problems such as 91, 97 can be answered directly without having to solve much. 83 is recursive combinatorics.

Scoring:
Combinatorics > Number Theory > Algebra > Geometry.

I need to pra

One of my peers who had outstanding scores in problem sets of such style suggested to me this book (and few other mathematical circles' books, which I haven't flipped through and are for much later). It's like a half month crash course.


I have always wanted to complete reading and attempting the problems in this book.

Getting the diagrams right enhances the ability to push through to a solution (problem 55, for instance).

Problem 57 is an application of Menelaus's and Ceva's theorem whereas Ptolemy's theorem is applied in 65. Drawing instrument box comes handy for problems 59 (and 60).

After a point I simply read through the solutions of some of the problems because I couldn't bear staring any longer.

Most of the problems require application of tricks, rearrangements or substitutions which makes looking for clues in the problem statement important. Few require a combination of theorems to reach the end result, whereas some problems such as 10, 11 (similar to 18) require none.

Problems 5, 20, 27, 30, 32, 37 could be solved in the head. I couldn't solve 9 and 17 or get the upper bound in 35 and 42 with aid.

My fav

Geometry has direct real world applications, and it is also the most dreaded (by me). Although the problems pertain to Euclidean geometry which is prevalent in architecture, I have found most use of differential geometry: machine learning (gradients), design (surfaces and 3d-modelling) and more.

Aiming for solving at least one in three without hints. I might want to share interesting problems.

I like mountaineering too, except for the steeper parts. As opposed to a problem book, this book also provides guidance.

One of my old exercises:
If every task (group) has its disjoint sets of requirements and precautions (likes and dislikes), then form a pair of sets of requirements and precautions (likes and dislikes) an individual should adopt to complete maximum tasks in succession (join most groups at once).

It is important to disregard any presuppositions about the difficulty of the problems (especially those that are binned together) because one risks anchoring other problems with another difficult problem (which could not be solved), and they may not give enough thought to each subsequent problem before moving on or skipping the entire set.

Practical applications can be contested - I have found certain topics to be quite useful and hope to get a boost in completion of other goals. It would be more difficult if problems were given out of the blue. Few unyielding ones of the many:

I: 15; II: 10 and 17 are similar, 22; VIa: 21; XIXa: 9, 11, 19, 20 and a large part of XIXb; XX: 8; XXIa: 7; XXIb: 10, 12; XXIIa: 14, 15 is similar to 10 of XXIIb; XXIII: 25, 2

Alright, I have come to a realisation that instead of memorising the toolkit (like I used to do before), deriving, to a certain extent, each of the mathematical assertions, likely expands intuition, and may improve success rate for coming up with solutions for the graded problems.

Limiting values, convergence, divergence, series become part of introductory undergraduate courses.

Probability (including inverse) and inequalities are my favourites.

Few chapters, such as surds, miscellaneous equations (including indeterminate ones) and determinants can be tiresome. I might want to list out all the problems that took me longer than expected.

Mathematics is meditation. Many may love problems but solutions may not favour most - in such circumstances one must (like most others) skip the tougher ones initially - it has the effect of momentarily pushing aside all the other individual troubles.

Combinatorics is my favourite. This book contains problems from Tripos.

Small parameter based learning, statistics algorithms can be trained on personal machine, and then ported to embedded targets in ONNX or C using emlearn and TFlite. LLMs (AI) come to rescue for generating other C programs (such as spiders or finding correct plaintext for a hashcode from a large list), which are noticeably quicker in low clock rate microcontrollers (compared to C++). VHDL is more familiar (to me).

Although I have tried KiCAD for gerber, LibrePCB, which I have been using for hobby projects, is not mentioned. I have used free version of Quartus Prime for Max10.

There may be more ways to achieve the same task, for instance, I prefer reed relays over BJTs to compartmentalise actuator circuit from controller circuit, especially for one-time events such as unconventional shutdown, ballast blow, spoilers.

One of the problems (for which my solution is not optimal):

Given a rectangular planar surface, divided into grid-space with each grid square side a common factor of side lengths of all the rectangular parts (or group of parts) that are supposed to be placed on that surface, determine the placement connected by wires of one grid square thickness:

- Minimise wire length
- Maximise distance between heat dissipators

Friendly. References to QM, Modern and Thermal Physics makes it more so. Polynomials (quadratic) and complex numbers become important. It is possible to use ICs with OpAmps instead of a signal generator for input. On large circuits, I prioritize checking the outputs (using DMM on breadboard) only around those components that are scarce. I used to write my own programs but the circuit simulators mentioned are good.

Part 3 gets engrossing by the page: business houses, prominent people, repealed ACTs, and corporations (manufacturing, synthetics, technology and pharmaceuticals).

The author travels a lot - waiting list for flight tickets was new to me - airport must have felt like train station - should have taken a bus.

It gets increasingly opinionated, and problems with prospective solutions are bombarded.

The book mentions most of the treaties, frameworks, member nations and procedures. D. Malone is quoted often.

Now that my memory has been jogged, I remember reading and watching television about most of the events.

2001 is the earliest I can recall, and the most intense. An earthquake at the start of the year, sanctions continued, plane hijacks in a far away land, and the western theatre was nearly lit.

"It is no wonder that Bombay’s vision was ignored. It was too practical and sensible—much like Bombay’s citizens."

Mistakes are expensive. Few have time to dilly dally.

"Instead of going back to my desk, I went out into the street and wandered aimlessly toward the harbor, feeling defeated."

La land de la wanderers.

Preventive detentions have made amazing authors out of noteworthy individuals (of democratic stature), who would have otherwise ferociously debated and pointed fingers at one another (figuratively) on the legislative floors, instead of being obligated, by virtue of boredom, to delegate time towards applying literary skills in assimilating information: as what has, in the confines of desolate walls, lead to this book.

Comparative study with numbers may not tell the whole story. Few entities censure data until much later when it's effect would most likely be dimmed down. When a certain kind of negative events become regular occurrences, it insinuates apathy which leads to delayed resolution.

Lot of doomsday signalling.

Why not a fast tiger and an enduring elephant; like a quantum superposition.

"[...] Alexander reassured his men that they were doing all this for the sake of glory— [...] talk and write about them." Alexander was right.

"'Treat me . . . ' replied Puru." Puru was toiling for honour.

Macedonian Phalanxes, likely, had tough time taking on trumpeting elephants to deter futher inquisitions towards peninsular conquest.

Addictive.

Paying less heed to specific criticisms (which may be feelings rather than facts): Economics may not be an exact science, but to be formulated (especially the Macro kind) through centuries, from atrociously massive experiments of trials and errors, is dismal to the extent of being appalling.

Contrary to the expectations - based on Author's (Chacha Nehru) legal profession - of muddled, meandering and emotionally unscathed passages; this book nearly overflows with sensational articulation.

Parameters such as α, n, γ, λ can be picked by trials (n ~ 5 in most cases), instead of grid search, as they seem fairly independent. Methods can be specific to the problem (which maybe a prediction or control, amongst others) with tradeoffs between latency and memory. LLMs help with method selection, discretisation and reduction of state-action space to explore feasibility of ideas.

Had to relearn backgammon.