PREFACE

God used beautiful mathematics in creating the world. - Paul Dirac

The world we live in is a crowned jewel of the creator, the Kohinoor that adorns and spreads the light of life, which in its various manifestations includes the mother earth, that by its own right is the queen of all creations, being the most dynamic abode, nurturing & accommodating the diverse passions of the creator.

"hiranmayena patrena

satyasyapihitam mukham 

tat tvam pushann apavrinu

satya-dharmaya drishtaye"

"O my Lord, Sustainer of all that lives, Your real face is covered by Your dazzling effulgence. Kindly remove that covering and exhibit Yourself to Your pure devotee. O Pushan, nourisher of all, please remove your glaring effulgence." (Isopanishad, Verse 15)

Unraveling the mysteries of creation is eternally evolving in which the human mind is the potent contributor. Of all forms of active articulation of internalized experiences, mathematics commands a niche for itself and no wonder, crowns itself, the Queen of the Sciences.

As the adage goes, “Beauty is in the eyes of the beholder”. It is the thin line that demarcates seeing from perceiving marking the subtle difference between matter and energy, physical and the metaphysical, concrete and the abstract, and, going a step further, the material and the spiritual. But seeing and perceiving are still limited to the individual and, to use a mathematical expression, a local concept. The experiences cannot be universalized unless appropriately articulated. "Seeing" (with all 5 senses), perceiving and articulating are the three integral components of “knowing”. Knowledge-sharing, which is the core of the learning process, has its parameters laid down thus. Any teacher, especially a mathematics teacher, has to be well-armed with the art of articulating and presenting a perception appropriately enough to invoke the latent potential of the learner, to seek and strive until enlightenment and internalization are achieved.

Amidst all hue and cry about the negatives of the lecture method, the teaching fraternity has been misled by the overemphasis on “hands-on” vis-à-vis the ultimate comprehension. The learning goals have suffered a setback and have not been able to reach beyond perhaps “seeing”. Even this phase only partially traversed leaving all learning piecemeal.

Now let us not get into half-baked conclusions, I am not advocating monotonous one-sided deliveries of information from outside. It is meaningful conversation that should set the tone and direction of drawing out the consciousness embedded in the innermost recesses of each potentially divine individual. The teacher just leads with a light, hand-holding initially. But then he is more a partner than the leader in the entire path to be traversed. It is the art of initiating and sustaining this dialogue with the student that makes a teacher’s efforts worthwhile.

As an author of mathematics textbooks I would like to share my experience as a teacher while recommending the linguistic abilities a mathematics teacher should acquire. I find Jean Piaget putting it in a nutshell - “Logic and mathematics are nothing but specialized linguistic structures”, and which gels with Richard Courant’s “Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality."

The text books have been made differently in the following aspects:

• They are not class-wise but discipline-wise.

• The different branches of mathematics have been discussed from the basic introductory class till the levels catering to class 12.

• The logical perception in the need and evolution of each of these branches has been endeavoured all along.

• The treaded path is more of a teacher than an author.

• It is intoned with nascent philosophical thoughts untinged by borrowed views.

• While preserving the rigours of mathematical discipline, the endeavour has been towards an interactive and soulful warming up, before dealing with the hard-core frigidity of the routine and the rhetoric.

• Hence the perusers, especially the teachers, are entreated not to ignore the introductions as not being examination-worthy.

• In fact, it is in such discussions that conceptual facets will emerge in their holistic ramifications and come in handy when required for application on different warfronts of attacking a problem.

• Some secrets of problem-solving have been revealed specific to the branches, as to where the eye of the bird is located for the Arjuns of the battlefield. Please refer to the section on Algorithm of Problem-solving.

• There are hyperlinks built-in to the textbook, suitable for e-learning as well. I hope among the ensuing pages, I have lived up to the expectations of Richard Courant according to whom, “Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality”.

Before knowing the textbooks, know the author, Chitralekha Gurumurthy, Retd. Joint Commissioner, KVS and former Director Academics, CBSE (Central Board of Secondary Education), India.

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