the art of problem solving the basics

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The Art of Problem Solving: The Basics Paperback – Jan. 1 2006

• Part of series Art of Problem Solving
• Print length 272 pages
• Language English
• Publisher AoPS Inc.
• Publication date Jan. 1 2006
• Dimensions 21.59 x 1.91 x 27.94 cm
• ISBN-10 0977304566
• ISBN-13 978-0977304561
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About the author, product details.

• Publisher ‏ : ‎ AoPS Inc.; 7th edition (Jan. 1 2006)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 272 pages
• ISBN-10 ‏ : ‎ 0977304566
• ISBN-13 ‏ : ‎ 978-0977304561
• Item weight ‏ : ‎ 658 g
• Dimensions ‏ : ‎ 21.59 x 1.91 x 27.94 cm
• #406 in Business Decision-Making & Problem Solving (Books)

About the author

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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The Art of Problem Solving: The Basics: 1 Paperback – 31 Aug. 2006

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• ISBN-10 0977304566
• ISBN-13 978-0977304561
• Edition 7th
• Publisher Aops Inc
• Publication date 31 Aug. 2006
• Part of series Art of Problem Solving
• Language English
• Dimensions 21.59 x 1.91 x 27.94 cm
• Print length 272 pages
• See all details

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Product details

• Publisher ‏ : ‎ Aops Inc; 7th edition (31 Aug. 2006)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 272 pages
• ISBN-10 ‏ : ‎ 0977304566
• ISBN-13 ‏ : ‎ 978-0977304561
• Dimensions ‏ : ‎ 21.59 x 1.91 x 27.94 cm
• 8,106 in Education Studies

About the author

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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ISBN: 1885875002

ISBN13: 9781885875006

The Art of Problem Solving Vol. I: The Basics Solutions

(part of the aops competition preparation series ).

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The Art of Problem Solving, Volume 1, is the classic problem solving textbook used by many successful MATHCOUNTS programs, and have been an important building block for students who, like the authors,... This description may be from another edition of this product.

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How to Solve It

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Mathematics

How to Solve It: A New Aspect of Mathematical Method

• John H. Conway

The bestselling book that has helped millions of readers solve any problem

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A must-have guide by eminent mathematician G. Polya, How to Solve It shows anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can help you attack any problem that can be reasoned out—from building a bridge to winning a game of anagrams. How to Solve It includes a heuristic dictionary with dozens of entries on how to make problems more manageable—from analogy and induction to the heuristic method of starting with a goal and working backward to something you already know. This disarmingly elementary book explains how to harness curiosity in the classroom, bring the inventive faculties of students into play, and experience the triumph of discovery. But it’s not just for the classroom. Generations of readers from all walks of life have relished Polya’s brilliantly deft instructions on stripping away irrelevancies and going straight to the heart of a problem.

"Every prospective teacher should read it. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: 'He writes a, he says b, he means c; but it should be d.'"—E. T. Bell, Mathematical Monthly

"[ How to Solve It ] shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected."—Herman Weyl, Mathematical Review

"I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it."— Scientific Monthly

"Every mathematics student should experience and live this book"— Mathematics Magazine

"In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let's hope this classic will remain a source of inspiration for several generations to come."—A. Bultheel, European Mathematical Society

“Every mathematics student should experience and live this book.”— Mathematics Magazine

“[ How to Solve It ] shows anew how keen its author is on questions of method and the formulation of methodological principles. Exposition and illustrative material are of a disarmingly elementary character, but very carefully thought out and selected.”—Herman Weyl, Mathematical Review

“Any young person seeking a career in the sciences would do well to ponder this important contribution to the teacher’s art.”—A. C. Schaeffer, American Journal of Psychology

“I recommend it highly to any person who is seriously interested in finding out methods of solving problems, and who does not object to being entertained while he does it.”— Scientific Monthly

“Every prospective teacher should read [ How to Solve It ]. In particular, graduate students will find it invaluable. The traditional mathematics professor who reads a paper before one of the Mathematical Societies might also learn something from the book: ‘He writes a, he says b, he means c; but it should be d.’”—E. T. Bell, Mathematical Monthly

“In an age that all solutions should be provided with the least possible effort, this book brings a very important message: mathematics and problem solving in general needs a lot of practice and experience obtained by challenging creative thinking, and certainly not by copying predefined recipes provided by others. Let’s hope this classic will remain a source of inspiration for several generations to come.”—A. Bultheel, European Mathematical Society

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Books that have problems requiring ingenuity but doesn’t require specific field knowledge

The type of problems I’m looking for should be a little bit easier than IMO questions, similar to the ones in “Problem-Solving Strategies” by Arthur Engel.

I’ve spent years being too obsessed in being rigorous that I didn’t realise that I was neglecting my problem-solving skills. Hence I want to change that.

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More From Forbes

First principles thinking: the blueprint for solving business problems.

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Founder and CEO at Stealth Scaling .

First principles thinking is a method of problem-solving that involves breaking down complex issues into their most basic and fundamental parts. Originating from ancient Greek philosophy and revitalized by modern thinkers like Elon Musk, it asks us to discard inherited assumptions and conventions. Instead, we're encouraged to rebuild from the ground up, deriving solutions from these foundational truths.

For founders, this means innovating beyond industry norms and creating products or services that genuinely resonate with market needs. For executives, it translates to strategies sculpted from a deep understanding of the company's core objectives rather than merely emulating competitors.

For business owners, it's about continuously reevaluating and refining operations, ensuring efficiency and relevance at every turn. In essence, first principles thinking isn't just a methodology—it's a mindset that enables leaders across the spectrum to navigate the volatile business terrain with clarity, originality and vigor.

How First Principles Helped Me Bootstrap And Scale My Business

In my early entrepreneurial days, I launched LiveVoice, a virtual receptionist platform. However, as challenges emerged, I didn't default to common practices. I adopted first principles thinking, reevaluating issues from their fundamental core without the influence of status quo biases.

Key decisions steered the course of my business. Shifting our call center from the U.S. to the Philippines was one, balancing cost with service quality. Recognizing the power of a name, I transitioned to "Order Solutions," capturing our essence and building trust. I also initiated split shifts for agents, optimizing their productivity during peak hours.

However, it wasn't just about problem-solving. It was about redesigning the approach. When I aimed to differentiate in a crowded market, I didn't mimic competitors. I asked foundational questions about our unique value. This led me to a niche: restaurant phone orders. In acquiring clients, I bypassed traditional ads. Instead, through deep questioning and brainstorming, I innovated with tactics like LinkedIn outreach and cold emails—yielding higher returns with lower costs.

Utilizing First Principles In Your Business Strategy

The power of first principles thinking isn't confined to my journey; it's a universally adaptable approach that can revolutionize any business strategy.

For example, Musk applied first principles to rethink battery costs for Tesla, not accepting the established pricing but breaking down costs to the component level. Similarly, Airbnb, instead of accepting the hotel industry's norms, stripped down the concept of accommodation and reimagined it, leading to the birth of peer-to-peer home sharing.

As a founder, executive or business owner, this methodology enables you to dissect complex problems, remove preconceived notions and build solutions from the ground up. It's not about tweaking the existing; it's about pioneering the new.

1. Define The Problem Clearly: Distill The Challenge To Its Core Essence

• Pinpoint the problem. Clarity is crucial. The sharper your problem statement, the better equipped you are to tackle it.

• Deep dive with "why." This is reminiscent of Toyota's " Five Whys " technique. By the fifth why, you often unveil the root issue. For example, if a software startup has a product not gaining traction, repeatedly asking "why" can uncover deeper issues like market fit or user interface problems.

• List assumptions. We all have them. Unearthing these assumptions can lead to epiphanies. SpaceX, for instance, reduced rocket costs by challenging the assumption that rockets can't be reused.

2. Deconstruct And Analyze: Examine Every Aspect Of Your Challenge

• Break it down. Divide the problem into fundamental parts. It's like understanding a car by studying its engine, wheels and body separately.

• Inspect each component. With no preconceived notions, analyze each part. This enables you to see where the real bottlenecks or inefficiencies lie.

3. Brainstorm Innovatively: Devise Bespoke, Pioneering Solutions

• Encourage team collaboration. Merge expertise from various fields in order to innovate. A mix of perspectives can lead to holistic solutions.

• Focus on the fundamental problem. This ensures your brainstorming remains directed and purposeful.

• Think outside the box. The success stories of companies like Dropbox were built on unconventional solutions to common problems.

4. Prototype And Validate: Bring Your Solution To Life And Vet Its Viability

• Build a minimal model. Create a basic version to understand its practicality. For digital startups, this could be a minimum viable product (MVP).

• Gather feedback. Use early user feedback to shape your solution. This should help ensure that it resonates with the intended audience.

5. Implementation And Iteration: Deploy, Assess And Fine-Tune

• Execute. Transition from theory to practice.

• Monitor. Use metrics and KPIs to assess progress.

• Iterate: Constantly refine the offering based on real-world use and feedback.

The transformative journey of my ventures underscores the sheer potency of first principles thinking. It's more than just a problem-solving tool; it's a paradigm shift, a way to unfetter oneself from the chains of convention and truly innovate.

However, the real beauty of this methodology is its adaptability. Whether you're a fledgling startup taking its first steps, a seasoned executive navigating a corporation through turbulent times or an intrepid business owner carving a niche, first principles thinking provides a structured, analytical approach to dissect challenges at their very root. It encourages us not just to find answers but to question the questions themselves and, in doing so, to craft solutions that are not only effective but pioneering.

As you charter the vast seas of the business world, let the compass of first principles guide you. It won't just show you the direction; it will illuminate a path filled with boundless possibilities.

Forbes Communications Council is an invitation-only community for executives in successful public relations, media strategy, creative and advertising agencies. Do I qualify?

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The Art of Problem Solving, Volume 1: The Basics Solutions Manual Paperback – August 1, 2006

• Part of series Art of Problem Solving
• Print length 144 pages
• Language English
• Publisher AoPS Incorporated
• Publication date August 1, 2006
• Dimensions 8.25 x 0.25 x 10.75 inches
• ISBN-10 0977304574
• ISBN-13 978-0977304578
• See all details

Editorial Reviews

About the author, product details.

• Publisher ‏ : ‎ AoPS Incorporated; 7th edition (August 1, 2006)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 144 pages
• ISBN-10 ‏ : ‎ 0977304574
• ISBN-13 ‏ : ‎ 978-0977304578
• Item Weight ‏ : ‎ 11.2 ounces
• Dimensions ‏ : ‎ 8.25 x 0.25 x 10.75 inches
• #92 in Mathematics Study & Teaching (Books)
• #1,005 in Education Theory (Books)

About the author

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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the art of problem solving vol. 1 the basics pdf

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The Art of Problem Solving, Vol. 1: The Basics Paperback – August 1, 2006

• Part of series Art of Problem Solving
• Print length 288 pages
• Language English
• Publisher AoPS Incorporated
• Publication date August 1, 2006
• Dimensions 8.5 x 0.75 x 11 inches
• ISBN-10 0977304566
• ISBN-13 978-0977304561
• See all details

Editorial Reviews

About the author, product details.

• Publisher ‏ : ‎ AoPS Incorporated; 7th edition (August 1, 2006)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 288 pages
• ISBN-10 ‏ : ‎ 0977304566
• ISBN-13 ‏ : ‎ 978-0977304561
• Item Weight ‏ : ‎ 1.45 pounds
• Dimensions ‏ : ‎ 8.5 x 0.75 x 11 inches
• #92 in Decision-Making & Problem Solving
• #144 in Education Theory (Books)

About the author

Richard rusczyk.

Richard Rusczyk founded Art of Problem Solving (AoPS) in 2003 to create interactive educational opportunities for avid math students. Richard is one of the co-authors of the Art of Problem Solving classic textbooks, author of Art of Problem Solving's Introduction to Algebra, Introduction to Geometry, and Precalculus textbooks, co-author of Art of Problem Solving's Intermediate Algebra and Prealgebra, one of the co-creators of the Mandelbrot Competition, and a past Director of the USA Mathematical Talent Search. He was a participant in National MATHCOUNTS, a three-time participant in the Math Olympiad Summer Program, and a USA Mathematical Olympiad winner (1989). He graduated from Princeton University in 1993, and worked as a bond trader for D.E. Shaw & Company for four years. AoPS marks Richard's return to his vocation: educating motivated students.

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• 5 star 4 star 3 star 2 star 1 star 2 star 75% 15% 4% 3% 3% 3%
• 5 star 4 star 3 star 2 star 1 star 1 star 75% 15% 4% 3% 3% 3%

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Customers say

Customers find the content challenging but educational. They also describe the writing style as well-written and good for kids.

AI-generated from the text of customer reviews

Customers find the book challenging but educational, with clear treatment of problem solving. They also say the chapters are useful and the book does not hesitate to talk about proofs and mathematical rigor.

"This book (and most likely the entire series) is fantastic. Concepts are explained fully and in the logical ordering necessary to build upon one..." Read more

"...layout of each chapter is very clear, and it is not that difficult to learn the challenge concepts since each topic starts with pretty basic..." Read more

"This book explains in great detail what I have learned, it is very helpful for my children to learn." Read more

"...It covers a very wide range of topics and does not hesitate to talk about proofs and mathematical rigor, which are some things that may never appear..." Read more

Customers find the writing style of the book well-written and clear.

"...The layout of each chapter is very clear , and it is not that difficult to learn the challenge concepts since each topic starts with pretty basic..." Read more

"Good book for kids. Well written . Classic book for learning essential math skills. I use it to teach my own kid." Read more

"I'm looking forward to learning from this apparently well-written , clear treatment of problem solving." Read more

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• Area around 55° 11' 31" N, 73° 10' 30" E /
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Drug resistance of different mycobacterium tuberculosis genotypes in the omsk oblast of russia.

• SHORT COMMUNICATIONS
• Published: 02 April 2024
• Volume 93 , pages 240–242, ( 2024 )

Cite this article

• A. A. Vyazovaya 1 ,
• I. V. Kostyukova 2 ,
• A. A. Gerasimova 1 ,
• D. R. Terentieva 1 ,
• O. A. Pasechnik 3 &
• I. V. Mokrousov 1  

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A total of 397 strains of Mycobacterium tuberculosis isolated from newly diagnosed patients with pulmonary tuberculosis in the Omsk oblast in 2019–2020 were genotyped. The prevalence of the Beijing genotype strains (70.8%), in particular, of two modern sublineage clusters: Central Asian/Russian (46.1%) and B0/W148 (19.1%), was established. Strains of the ancient sublineage of the Beijing genotype were represented by clusters 1071-32 and 14717-15, totaling 4.8%. Compared with other genotypes, the strains of B0/W148-cluster and the ancient Beijing sublineage were more often characterized by multidrug resistance (MDR): 93.4 and 94.7%, respectively ( P < 0.0001). Among members of other genetic families (LAM, Ural, T, Haarlem), drug-sensitive strains predominated (75.0%). The circulation of MDR Beijing strains requires molecular epidemiological surveillance in view of their possible wider spread.

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This study was supported by the Russian Science Foundation, project no. 19-14-00013.

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St. Petersburg Pasteur Institute, 197101, St. Petersburg, Russia

A. A. Vyazovaya, A. A. Gerasimova, D. R. Terentieva & I. V. Mokrousov

Clinical Antituberculosis Dispensary, 644058, Omsk, Russia

I. V. Kostyukova

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Vyazovaya, A.A., Kostyukova, I.V., Gerasimova, A.A. et al. Drug Resistance of Different Mycobacterium tuberculosis Genotypes in the Omsk Oblast of Russia. Microbiology 93 , 240–242 (2024). https://doi.org/10.1134/S002626172360444X

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Received : 09 October 2023

Revised : 09 November 2023

Accepted : 10 November 2023

Published : 02 April 2024

Issue Date : April 2024

DOI : https://doi.org/10.1134/S002626172360444X