Limit Infinite

My favorite things – Books

Good books that I have read are:

Promising books that I like to read are:

A Course of Pure Mathematics is a classic text book of mathematics by the English mathematician G H Hardy. True to the spirit of the “Pure Mathematics” in the title, the book makes no assumptions in its treatment of the subject. The book gives a fundamental treatment to the topics of calculus.

e: The Story of a Number gives a history of mathematics of the last 500 years or so. In giving the history, it gives brief details of the lives of mathematicians such as Descartes, Fermat, Napier, Newton and Leibniz as well as how the mathematical concepts gradually evolved. The most significant development in mathematics in this period was calculus. Worth mentioning of this book is in particular a good treatment of the development of ideas of calculus by Newton and Leibniz and the contention between the two for the credit over the invention of the subject.

It gives you answers to questions such as why the new mathematical inventions were done and how the great areas of today’s mathematics were a result of many mathematicians’ quest for knowing the answers to age old questions (such as squaring the circle or a hyperbola) rather than one mathematician conjuring up the seemingly difficult ideas of fields such as calculus out of the blue. Since it describes the mathematical concepts from their historical development point of view, it gives a very nice intuitive justification to each of them.

The strength of this book is in not limiting to just the lives of mathematicians (unlike some other math history books) and in covering the evolution of mathematical concepts in general. After reading the book, I had a sincere appreciation for the minds of mathematicians and a renewed understanding of the concepts of limits, the inverse problems of finding a derivative(slope of a curve’s tangent) and integration(area under a curve), binomial theorem and of course, the beautiful number ‘e’.

A Mathematician’s Apology is an essay trying to give a justification of why Mathematics is pursued, not so much from the viewpoint of its applicability, but from the viewpoint of its beauty and its ability to give emotional satisfaction to the pursuers. Applicability of Mathematics needs no justification, so it was reasonable for Hardy to take up the task of justifying a pursuit of Mathematics for its own sake (aka Pure Mathematics).

I had read Hardy’s ‘A course of Pure Mathematics’, and I had read several anecdotes on Hardy. Having loved all of them, I had high expectations from the current essay. I must say this essay was a big disappointment. I felt Hardy dwelt too long on some vague nuances without making an appealing point.

Here are some examples. Hardy relates a pure mathematician’s pursuit to that of physician. While a physician’s work is beneficial to the humanity, a person is not in that profession constantly mindful of the greater good his profession does. A physician may have reasons such as intellectual curiosity, pride, fame and money, and while these may seem mundane, they are nothing to be ashamed of. Towards the end of the essay, Hardy talks about the effect of Mathematics of war and digresses slightly to a discussion on warfare itself.

I felt Hardy would have better achieved what he sought out to do by giving more examples of beauty from Mathematics or some interesting anecdotes from his life or the lives of other Mathematicians.

I did like the foreword by Dr.Snow which gave a brief biography of Hardy.

Capitalism: The unknown ideal gives you a good understanding of Ayn Rand’s philosophy. The core of Ayn Rand’s philosophy is a minimal government role in the society. It says the society is better off with no government regulation in markets driven by demand and supply and even in spheres such as education. By definition, government is able to use brute force(violence) to exercise its defined powers and this is unique to a government among all elements of a society including individuals or groups (such as corporations). Thus, by having excessive role of government in a society lets this particular element of the society advance its agenda by unfair means (force). For example, in education, government may push a prescribed curriculum (with, say, a religion bias) without giving parents a choice on how they want their children to be educated. Further, government employees are just human and hence there is no reason to think they are more morally responsible than other elements of the society. Higher government role breeds corruption in the society by letting favoritism by government of specific individuals or groups over others creep in.

The philosophy advocates a society based on free will and choice. Markets are driven by demand and supply. Hence, consumers choose the best product and producers have incentive to produce the best product (or service). It says that if individuals and groups (think corporations) are let free to exercise their enterprise and selfish motives, competition among individuals and corporations automatically brings out the best benefits for consumers (society). Corporations can not afford to produce low quality products or services lest they should lose the good will of their customers. Thus, there is no need for regulation by agencies such as FDA or SEC.

The book says that the only role for government in a society is to protect the rights of individuals, groups (corporations) and of the a nation.

There are a few aspects that the book does not fully convince me on. How does the philosophy ensure that a corporation with dominance in one market area does not use its position to acquire dominance in another area? Big corporations with a monopoly (whether coercive or non-coercive) have a position that they can use to get an unfair advantage over other players. How does the philosophy ensure that corporations do not exploit non-human elements such as environment or animals? If global warming was indeed true (say), what forces the corporations to refrain from behavior causing it in the absence of agencies such as EPA? May be, private equivalents of EPA would spring up giving public the required awareness and forcing corporations to be environmentally responsible – just like corporations try to claim green for more good will of customers, corporations would want to claim certification from these private EPAs.

While many of the essays in the book were written by Ayn Rand, the book has some essays written by others including Alan Greenspan. One particular essay worth pointing is of Alan Greenspan where he advocates having the banking backed by gold rather than unlimited issue of credit.

Whatever view you take of free markets and government role, the book is a lucid presentation of one extreme view on the topic. I highly recommend this book to any one who likes to take a position on this topic, but be educated of both sides before hand.

The Law was written in 1850 by Frederic Bastiat, a French economist and statesman. In this, he argues emphatically against socialism, how the role of government must be restricted to merely preventing injustice, and how government should not take a broader role such as sponsoring welfare schemes, education, religion, etc. Preventing injustice is defined merely as preventing exploitation in any form of individuality, liberty or property of people.

Inherently, government is empowered with ability to use force, and any responsibility beyond preventing injustice amounts to using force to plunder. For example, sponsoring a welfare scheme requires collecting taxes (seize property by force) from those who do not necessarily benefit from such a scheme.

He points out arguments from some socialists where in the absence of government hand (law), the society degrades into purely individualistic, atheistic or pursuing irrelevant education (of Hindus and Turks). He also points out how socialists view legislators to be God-like, while rest of the mankind being passive. And, he argues humans as not being mere machines, but with freedom, they act voluntarily to help others, choose their own religion, education and can contribute with the best of their faculties.

The Greatest Show On Earth by Richard Dawkins claims to provide evidence to the theory of evolution. True enough, the book gives several convincing examples. Very-different-looking breeds of dogs result as breeders sculpt the gene pools. Lizards of Pod Mrcaru islet were observed within a small period of 36 years to have evolved to show noticeable differences (for example, in jaw sizes). Then, the human body as well as bodies of other biological creatures has several imperfections, one of which is the obviously absurd detour taken by the vas deferens from the testis to the penis. Such imperfections could only be the result of an incrementally-adjusting-process such as evolution rather than of a well-thought-out intelligent design.

To many, the theory of evolution is inconceivable because of the marked physical differences between different creatures. How could a human being evolve from such a being as fish? That is laughable to many. To me, the first convincing thought for evolution was that different dog breeds look so very different outwardly, but breeders can breed one into another. Then, I see that despite the marked outward differences there are striking internal similarities (for example, in the skeleton structures among vertebrates).

Any scientific theory falls apart if a theoretical prediction it makes fails in the real world. Dawkins argues that there are strong theoretical expectations from the theory evolution on certain similarities of genes between certain species, and real-world observations confirm each one of the expectations.

Dawkins explains how natural selection, as opposed to human action as in the case of dog breeding, is the agent of evolution of so many different species.

Along the way to making his case, Dawkins gives good knowledge about things such as tree rings, carbon dating and techniques (such as heating the DNA to separate the two helices) used for estimating similarity of genes between species.

Radio Access Networks for UMTS: Principles and Practice is comprehensive on the subject. While 3GPP specifications are the reference for the details of 3G wireless communications, the extraordinary value that this book brings to the reader is that it puts the details in context. It follows a top down approach and is as if the author is walking you in a face-to-face training through the structure of the 3GPP details. In places where the structure of 3GPP details is unclear or confusing (I quote some instances below), the author gives enough context and emphasis which helps the reader establish a big picture and remember the details.

In cellular communications world, there are unique challenges to address. Quality of the signal over the air between the base station and the UE(cell phone) is affected by the surrounding environment, mobility of the UE and interference from other UEs, among other things. Battery power of the UE is also a premium resource and needs to be optimally used. These challenges impose the constraint that the cellular communications adapt dynamically to a fast changing environment. The cellular communications’ specifications must facilitate this adaptation. For example, in 3GPP specifications there are physical layer channels called Common Pilot Channels (P-CPICH and S-CPICH) which serve as reference for monitoring the signal quality. In addition, for certain channels there is a feature called inner loop power control which allows transmission power of signal to be adjusted 1500 times a second. The layers of communication stack (layer 1 – physical layer, layer 2 – transport layer, layer 3 – logical layer) are designed to work through these unique challenges. In addition to addressing the unique challenges, the cellular communications had to evolve over the years to meet the ever increasing demands for high data throughput. In summary, the cellular communication details are a complex beast.

In addition, in some instances, unlike the text book concepts of networking layers, the layering in 3GPP stack is somewhat blurred. For example, text book concept of physical layer’s responsibility is just to transmit signal at the required throughput. However, a responsibility of HS-SCCH physical layer channel is to transmit UE identity in case of HSDPA. Further, concepts of radio bearers and channels overlap. For example, there is a concept of signalling radio bearer (SRB) and the 3GPP specifications define multiple SRBs (SRB0, SRB1 and so on). Different SRBs are transmitted by different logical channels and hence have different flow of data through the stack.

3GPP specifications are indeed the reference for the details. However, the specifications are in many instances terse and lack context. A person without history of 3GPP evolution will be left gaping if he/she just reads through the specifications. Even if he/she is able to obtain details from the specifications, appreciating and remembering the details a few months after reading the specifications is nearly impossible. This is where the book comes in. The book covers the entire swath of topics relevant to UMTS radio access networks. The topics covered include the big picture of where UE, base station, RNC and core network sit, definition of 3GPP’s esoteric nomenclature such as Non-access stratum, Signalling radio bearer, radio access bearer and Node B, the flow of data among RNC, base station and UE, description of RRC states, details of layer 2, layer 3 as well as the physical layer.

Because the book covers in amazing detail and gives the surrounding context, I highly recommend this book for understanding UMTS radio access networks. I suspect this is the only book one will ever need on the subject.

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