problem solving strategies by engel

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Problem-Solving Strategies Paperback – Illustrated, Dec 12 1997

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• ISBN-10 0387982191
• ISBN-13 978-0387982199
• Edition 1st ed. 1998. Corr. 2nd printing 1999
• Publisher Springer
• Publication date Dec 12 1997
• Part of series Problem Books in Mathematics
• Language English
• Dimensions 15.49 x 2.39 x 23.29 cm
• Print length 413 pages
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• Publisher ‏ : ‎ Springer; 1st ed. 1998. Corr. 2nd printing 1999 edition (Dec 12 1997)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 413 pages
• ISBN-10 ‏ : ‎ 0387982191
• ISBN-13 ‏ : ‎ 978-0387982199
• Item weight ‏ : ‎ 590 g
• Dimensions ‏ : ‎ 15.49 x 2.39 x 23.29 cm
• #152 in Science Dictionaries
• #222 in Mathematics Study & Teaching
• #1,158 in Mathematics Textbooks

About the author

Arthur engel.

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Problem-Solving Strategies Paperback – September 20, 2013

• Print length 416 pages
• Language English
• Publisher Springer
• Publication date September 20, 2013
• Dimensions 6.14 x 0.85 x 9.21 inches
• ISBN-10 1475789548
• ISBN-13 978-1475789546
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• Publisher ‏ : ‎ Springer (September 20, 2013)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 416 pages
• ISBN-10 ‏ : ‎ 1475789548
• ISBN-13 ‏ : ‎ 978-1475789546
• Item Weight ‏ : ‎ 1.28 pounds
• Dimensions ‏ : ‎ 6.14 x 0.85 x 9.21 inches
• #140,981 in Mathematics (Books)

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Problem-solving strategies

By arthur engel.

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Problem-Solving Strategies is a unique collection of competition problems from over twenty major national and international mathematical competitions for high school students. The discussion of problem-solving strategies is extensive. It is written for trainers and participants of contests of all levels up to the highest level: IMO, Tournament of the Towns, and the noncalculus parts of the Putnam competition.

It will appeal to high school teachers conducting a mathematics club who need a range of simple to complex problems and to those instructors wishing to pose a "problem of the week," "problem of the month," and "research problem of the year" to their students, thus bringing a creative atmosphere into their classrooms with continuous discussions of mathematical problems.

This volume is a must-have for instructors wishing to enrich their teaching with some interesting nonroutine problems and for individuals who are just interested in solving difficult and challenging problems.

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Includes bibliographical references (p. [397]-398) and index.

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Problem Solving Strategies Paperback – 1 January 2003

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• ISBN-10 8181280156
• ISBN-13 978-8181280152
• Publisher anebooks - Springer
• Publication date 1 January 2003
• Language English
• Print length 426 pages
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• Publisher ‏ : ‎ anebooks - Springer (1 January 2003)
• Language ‏ : ‎ English
• Paperback ‏ : ‎ 426 pages
• ISBN-10 ‏ : ‎ 8181280156
• ISBN-13 ‏ : ‎ 978-8181280152
• Item Weight ‏ : ‎ 521 g
• Country of Origin ‏ : ‎ India
• Best Sellers Rank: #592,007 in Books ( See Top 100 in Books )

About the author

Arthur engel.

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Customers find the book ideal for students preparing for math olympiads. They say it presents a wide range of problems and strategies to solve them. Readers also mention the solutions are provided. Overall, they say the book is well worth the price.

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Customers find the book ideal for students preparing for the math olympiads. They say it's good for regional, national, and international levels. Readers also mention it'll be excellent for IIT students.

"... Very Good for Regional Mathematical olympiad , then to inmo and proceeding towards international level of excellence." Read more

"This book contains the hardest maths problem. Excellent for IIT students " Read more

" Good content for mathematics problem tackling ." Read more

"Contains all basic math problems... suitable for Olympiad-aimed students " Read more

Customers find the problems in the book wide-ranging and clear. They also appreciate the strategies to solve them.

"First of all, this book presents a wide range of problems and strategies to solve them...." Read more

"...There are a numerous problems , most of the, challenging and some just what un say standard ones...." Read more

"This book is a godsent , problems are very clear and intersting ." Read more

"The book is awesome. The solutions to the problems are provided ." Read more

Customers say the book is well worth the price.

"Anyone interested in competitive math must have a copy — well worth the price ." Read more

"A bit costly but worth every penny . This book is written beautifully. Tough for beginners but really grat book" Read more

"Here its cost is very low as compare to other websites. And brilliant book with required brilliant minds" Read more

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Problem-Solving Strategies

Arthur Engel | 4.42 | 175 ratings and reviews

Ranked #78 in Problem Solving

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Solving Puzzles, Not Problems: 5 Strategies for Growth in the Age of Change

As a leader, how do you approach challenges in your organization? Do you see them as problems to be solved, or puzzles to be pieced together? In today’s rapidly evolving technological landscape, this distinction could be the key to unlocking innovation and thriving in uncertain times.

The shift from problem-solving to puzzle-solving isn’t just a change in terminology – it’s a fundamental shift in mindset that can transform how your team tackles complex issues. Let’s explore why this matters and how you can implement it in your organization.

Why Puzzle-Solving Matters for Modern Leaders

1. holistic perspective.

Puzzle-solving encourages leaders to step back and consider all possible pieces before jumping to solutions. This holistic view is crucial when dealing with the multifaceted challenges presented to the modern leader.

2. OPPORTUNITY MINDSET

The Japanese business philosophy kaizen sees problems or challenges as a crucial step in the cycle of improvement. Puzzle-solvers adopt this frame of mind and see difficulty as an opportunity for growth and improvement.

3. EMBRACING DIVERSITY

Puzzle-solving thrives on diverse perspectives. By bringing together varied viewpoints, you can uncover pieces of the puzzle you didn’t even know were missing.

4. CONTINUOUS GROWTH

Puzzle-solving doesn’t just shift us into an opportunity mindset – it also fosters a culture of continuous learning and adaptation. As you piece together each new puzzle, you and your team grow in knowledge and capability.

Puzzle-Solving in Action

Let me share a personal experience that illustrates the power of this approach. During an organizational development event, our team faced the challenge of reducing a contract closure process from several weeks to just two days – a goal that initially seemed impossible.

Instead of being overwhelmed, we reframed the challenge by asking, “What must be true to achieve a two-day turnaround?” This shift in perspective allowed us to rethink the entire process and innovate a solution that met the ambitious target.

By approaching the challenge as a puzzle rather than a problem, we identified aspects of the process we hadn’t previously considered. We brought together team members from different departments, each offering unique insights. This diversity of perspective, combined with a willingness to question our assumptions, led to a breakthrough that transformed our operations.

How to Shift to a Puzzle-Solving Mindset

1. reframe challenges as growth opportunities.

Train your team to see “red” on a scorecard not as a failure, but as an area ripe for improvement and personal growth. This simple reframing can dramatically change how your team approaches challenges.

2. IDENTIFY MISSING PIECES

Before jumping into solution mode, ask, “What information or perspectives might we be overlooking?” This critical thinking approach can reveal crucial insights and areas for development.

3. ASSEMBLE DIVERSE TEAMS

Bring together people from different functions, backgrounds, and thinking styles to enrich your problem-solving process and foster mutual growth.

4. LEVERAGE AI FOR DIVERSE PERSPECTIVES

Use generative AI tools to access a wealth of existing knowledge and frameworks. This can provide you with an unprecedented number of lenses through which to examine a challenge and grow your understanding.

5. CREATE A CULTURE OF CURIOSITY AND GROWTH

Foster an environment where asking questions, seeking out new viewpoints, and continuous learning are encouraged and rewarded.

Growth is the only guarantee that tomorrow will be better. John C. Maxwell

The Future of Leadership in the Face of Constant Change

As we navigate the technological complexities of the modern era – including generative AI – the ability to shift from problem-solving to puzzle-solving will be a critical skill for leaders. This approach not only helps us tackle immediate challenges more effectively, but also reinforces our organization’s ability to adapt and innovate in the face of rapid technological change.

Remember, the goal isn’t just to solve the problem at hand, but to build a culture and mindset that thrives on complexity and change. By viewing challenges as puzzles and embracing diverse perspectives – both human and AI-generated – you’ll be better equipped to lead your team through the ever-changing landscape of modern business.

Your Challenge

What challenge are you currently facing that could benefit from a puzzle-solving approach? How might reframing this challenge and seeking out diverse perspectives lead to innovative solutions?

Take some time this week to practice puzzle-solving with your team. Start by reframing a current challenge as an opportunity, then brainstorm what pieces might be missing from your current understanding. You might be surprised at the innovative solutions that emerge.

Interested in discovering other practical growth tips to help you and your team keep pace with constant change?

Gain practical insights and discover real-world examples of how tools like AI can support your leadership development journey. Subscribe to the Maxwell Leadership blog for more content from AI researcher Daniel Englebretson and other professionals championing transformation in today’s marketplace.

About the author

Daniel Englebretson is an AI researcher, innovator, and entrepreneur. He is also the founder and CEO of Elynox, the co-founder and managing partner of ShiftHX, and an adjunct professor of artificial intelligence and communications at Wake Forest University and Elon University. Daniel is committed to empowering and enabling others with the skills and mindset shifts required to create opportunities to collaborate more effectively with AI.

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Solving numerical and engineering optimization problems using a dynamic dual-population differential evolution algorithm

• Original Article
• Published: 14 September 2024

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• Wenlu Zuo 1 , 2 &
• Yuelin Gao   ORCID: orcid.org/0000-0003-2021-2097 1 , 2  

Differential evolution (DE) is a cutting-edge meta-heuristic algorithm known for its simplicity and low computational overhead. But the traditional DE cannot effectively balance between exploration and exploitation. To solve this problem, in this paper, a dynamic dual-population DE variant (ADPDE) is proposed. Firstly, the dynamic population division mechanism based on individual potential value is presented to divide the population into two subgroups, effectively improving the population diversity. Secondly, a nonlinear reduction mechanism is designed to dynamically adjust the size of potential subgroup to allocate computing resources reasonably. Thirdly, two unique mutation strategies are adopted for two subgroups respectively to better utilise the effective information of potential individuals and ensure fast convergence speed. Finally, adaptive parameter setting methods of two subgroups further achieve the balance between exploration and exploitation. The effectiveness of improved strategies is verified on 21 classical benchmark functions. Then, to verify the overall performance of ADPDE, it is compared with three standard DE algorithms, eight excellent DE variants and seven advanced evolutionary algorithms on CEC2013, CEC2017 and CEC2020 test suites, respectively, and the results show that ADPDE has higher accuracy and faster convergence speed. Furthermore, ADPDE is compared with eight well-known optimizers and CEC2020 winner algorithms on nine real-world engineering optimization problems, and the results indicate ADPDE has the development potential for constrained optimization problems as well.

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Developments and Design of Differential Evolution Algorithm for Non-linear/Non-convex Engineering Optimization

Solving Constrained Non-linear Integer and Mixed-Integer Global Optimization Problems Using Enhanced Directed Differential Evolution Algorithm

An efficient modified differential evolution algorithm for solving constrained non-linear integer and mixed-integer global optimization problems, explore related subjects.

• Artificial Intelligence

Data availability

All the data in Sect.  6 are obtained under the same experimental setting. Then, the source code of CEC2013 test suite can be downloaded from https://github.com/P-N-Suganthan/CEC2013 . The source code of CEC2017 test suite can be downloaded from https://github.com/P-N-Suganthan/CEC2017-BoundContrained . The source code of CEC2020 test suite can be downloaded from https://github.com/P-N-Suganthan/2020-Bound-Constrained-Opt-Benchmark . The source code of the nine engineering problems can be downloaded in https://github.com/P-N-Suganthan/2020-RW-Constrained-Optimisation . We solemnly declare that all data in this paper is true and valid.

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Acknowledgements

This work was supported by the Key Project of Ningxia Natural Science Foundation (2022AAC02043), the First-class Discipline Construction Fund Project of Ningxia Higher Education (NXYLXK2017B09), the Major Scientific Research Special of North Minzu University (ZDZX201901), the 2023 Graduate Innovation Project of North Minzu University (YCX23075) and the Basic Discipline Research Projects Supported by Nanjing Securities (NJZQJCXK202201).

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Appendix A: Mathematical models of nine engineering problems

1.1 a.1 pressure vessel design, 1.2 a.2 rolling element bearing design, 1.3 a.3 tension/compression spring design, 1.4 a.4 welded beam design, 1.5 a.5 multiple disk clutch brake design, 1.6 a.6 step-cone pulley problem, 1.7 a.7 speed reducer design, 1.8 a.8 planetary gear train design, 1.9 a.9 robot gripper problem, rights and permissions.

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Zuo, W., Gao, Y. Solving numerical and engineering optimization problems using a dynamic dual-population differential evolution algorithm. Int. J. Mach. Learn. & Cyber. (2024). https://doi.org/10.1007/s13042-024-02361-7

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Received : 01 September 2023

Accepted : 20 August 2024

Published : 14 September 2024

DOI : https://doi.org/10.1007/s13042-024-02361-7

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