reverse mathematics john stillwell

The first book surveying the history and ideas behind reverse mathematicsReverse mathematics is a new field that seeks to find the axioms needed to prove given theorems. In Reverse Mathematics, John Stillwell offers a historical and representative view, emphasizing basic analysis and giving a novel approach to logic. By using a minimum of mathematical logic in a well-motivated way, Reverse Mathematics will engage advanced undergraduates and all mathematicians interested in the foundations of mathematics.

Objev podobné jako Reverse Mathematics - John Stillwell

How the concept of proof has enabled the creation of mathematical knowledgeThe Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems ... Unknown localization key: "more"

Objev podobné jako The Story of Proof - John Stillwell

Studying engineering, whether it is mechanical, electrical or civil, relies heavily on an understanding of mathematics. This textbook clearly demonstrates the relevance of mathematical principles and shows how to apply them in real-life engineering problems.It deliberately starts at an elementary level so that students who are starting from a low knowledge base will be able to quickly get up to the level required. Students who have not studied mathematics for some time will find this an excellent refresher.Each chapter starts with the basics before gently increasing in complexity. A full outline of essential definitions, formulae, laws and procedures is presented, before real world practical situations and problem solving demonstrate how the theory is applied.Focusing on learning through practice, it contains simple explanations, supported by 1600 worked problems and over 3600 further problems contained within 384 exercises throughout the text. In addition, 35 Revision tests together with 9 Multiple-choice tests are included at regular intervals for further strengthening of knowledge.An interactive companion website provides material for students and lecturers, including detailed solutions to all 3600 further problems.

Objev podobné jako Bird's Comprehensive Engineering Mathematics - John Bird

John Deere Gator s otevíracími dveřmi a sklopnou plošinou
přikrývka John Cotton Dreamium Eternal Love 220x200 cm
designový polštář John Cotton
přikrývka John Cotton CleanLiness
moderní koupelnové svítidlo Rabalux 5732 John
detailní model traktoru John Deere s vlečkou
realistický traktor Bruder John Deere
John Deere traktor Bruder Farmer
realistický traktor John Deere s otevírací kapotou
John Deere 7R řada model pro děti
Gary John Bishop sebezničující chování
John Deere Gator Bruder 1:16
Bruder 02491 John Deere Gator
hračka John Deere Gator pro děti od 4 let
stavební hračka John Deere
Tubbz John Wick kachnička

Now in its eighth edition, Bird’s Basic Engineering Mathematics has helped thousands of students to succeed in their exams. Mathematical theories are explained in a straightforward manner, supported by practical engineering examples and applications to ensure that readers can relate theory to practice. Some 1,000 engineering situations/problems have been ‘flagged-up’ to help demonstrate that engineering cannot be fully understood without a good knowledge of mathematics.The extensive and thorough coverage makes this a great text for introductory level engineering courses – such as for aeronautical, construction, electrical, electronic, mechanical, manufacturing engineering and vehicle technology – including for BTEC First, National and Diploma syllabuses, City & Guilds Technician Certificate and Diploma syllabuses, and even for GCSE revision.Its companion website provides extra materials for students and lecturers, including full solutions for all 1,700 further questions, lists of essential formulae, multiple choice tests, and illustrations, as well as full solutions to revision tests for course instructors.

Objev podobné jako Bird's Basic Engineering Mathematics - John Bird

John Deere Gator je detailně zpracovaný model v měřítku 1:16 z plastu. Vozidlo je multifunkční a vhodné pro hru na stavbách, v lese nebo v zemědělství. Je kombinovatelné s figurkami Bworld a obsahuje sklápěcí valník, volant a tažné zařízení.

• Detailně zpracovaný model v měřítku 1:16
• Multifunkční vozidlo pro různé scénáře hry
• Kombinovatelné s figurkami Bworld
• Vhodné pro děti od 4 let

Objev podobné jako Bruder 02491 John Deere Gator

Tubbz kachnička představuje miniaturu Johna Wicka v měřítku 5,5 cm s detailním provedením včetně černého obleku. Figurka je určena výhradně pro sběratelské a dekorativní účely. Není vhodná pro použití ve vodě nebo jako hračka.

• Miniaturní detailní zpracování postavy (5,5 cm)
• Věrné zachycení ikonického vzhledu Johna Wicka
• Ideální sběratelský kousek pro fanoušky
• Stylový dekorativní prvek do interiéru

Objev podobné jako Tubbz kachnička malá - John Wick

Model John Deere Gator od Bruder v měřítku 1:16 je detailně zpracovaná plastová hračka pro děti od 4 let. Vozidlo obsahuje funkční prvky jako sklápěcí valník, volant a tažné zařízení a je dodáváno s figurkou řidiče. Je vhodné pro různé typy herních scénářů včetně zemědělství, lesnictví a stavebnictví.

• Detailní model v měřítku 1:16 s vysokou věrností
• Multifunkční vozidlo vhodné pro různé scénáře hry (stavba, les, zemědělství)
• Obsahuje figurku řidiče a je kompatibilní s dalšími figurkami
• Funkční prvky: sklápěcí valník, volant, tažné zařízení

Objev podobné jako Bruder 02490 John Deere Gator s řidičem

Stavebnice LEGO Technic Kombajn John Deere 1470H obsahuje 117 dílků a je určena pro děti od 7 let. Model disponuje otáčivým ramenem, otevíracím drapákem na klády a pružícím podvozkem. Stavbu usnadňuje interaktivní návod v aplikaci LEGO Builder.

• Autentický model kombajnu John Deere s funkčními prvky
• Interaktivní 3D návod v aplikaci LEGO Builder usnadňuje stavění
• Vysoká pohyblivost díky otáčivému rameni a otevíracímu drapáku
• Odolný design s pružícím podvozkem pro realistickou hru

Objev podobné jako LEGO® 42218 Kombajn John Deere 1470H

Přepravník na dřevo John Deere od firmy Bruder je detailně zpracovaný plastový model v měřítku 1:16. Disponuje funkčním chapadlem pro 4 klády, otočným ramenem 360° a otevíratelnou kabinou. Hračka je vhodná pro děti od 3 let a je kombinovatelná s figurkami Bworld.

• Detailně zpracovaný model v měřítku 1:16 od německé firmy Bruder
• Funkční chapadlo pojme až 4 klády a má otočné rameno 360°
• Kombinovatelný s figurkami Bworld pro rozšíření hry
• Otevíratelná kabina s dveřmi a realistické pryžové pneumatiky

Objev podobné jako Bruder 02133 Přepravník na dřevo John Deere

Traktor Bonnie je šroubovací hračka pro děti od 3 let, která rozvíjí motorické schopnosti. Sada obsahuje traktor s přívěsem a kravičku na kolečkách. Všechny části jsou z plastu s bezpečnými zaoblenými hranami.

• Rozvíjí jemnou motoriku a koordinaci prostřednictvím šroubování
• Bezpečný design se zaoblenými hranami pro děti od 3 let
• Možnost kombinace s dalšími hračkami z řady Tomy John Deere
• Pohyblivá kolečka traktoru i kravičky pro snadné tlačení

Objev podobné jako Tomy John Deere Kids Postav si kamaráda - traktor Bonnie

Tubbz kachnička představuje postavu Johnnyho Castle z filmu Hříšný tanec v humorném pojetí. Figurka je vyrobena z vinylu a měří 9 cm na výšku. Jedná se o oficiálně licencovaný sběratelský předmět první edice.

• Oficiálně licencovaná figurka postavy Johnny Castle
• Detailní zpracování a věrné provedení
• První edice pro sběratele
• Vyrobeno z kvalitního vinylového materiálu

Objev podobné jako Tubbz kachnička Hříšný tanec - Johnny Castle (první edice)

Model John Deere Gator XUV 855D v měřítku 1:16 je detailní replika univerzálního terénního vozidla. Vyrábí se z odolných plastů a obsahuje funkční prvky jako sklopnou ložnou plochu a závěs. Je vhodný pro hru dětí v interiéru i exteriéru.

• Realistický detail: Otevírací dveře zavazadlového prostoru, sklopná ložná plocha a závěs pro přívěs.
• Vysoká odolnost: Vyrobeno z kvalitních, nerozbitných plastů, okna kabiny z průhledného odolného materiálu.
• Univerzální použití: Vhodné pro hru doma i venku, věrný model všestranného pracovního vozidla v měřítku 1:16.

Objev podobné jako Bruder John Deere Gator XUV 855D, 22,6 x 11,3 x 14 cm

Traktor BRUDER 3150 Farmer John Deere kombinuje nízkou hmotnost s vysokým výkonem. Model obsahuje realistické prvky jako otevírací kapotu a dveře. Díky kyvadlové nápravě a prodloužení řízení zajišťuje pohodlnou jízdu.

• Realistické detaily včetně otevírací kapoty a dveří
• Vynikající ovladatelnost díky vestavěné kyvadlové nápravě
• Kompatibilita s přívěsy ze zemědělské řady BRUDER
• Možnost přepravy postav bworld v kabině

Objev podobné jako Bruder 3150 Farmer traktor John Deere

Bruder 2032 Balíkovač John Deere je detailně zpracovaný plastový model v měřítku 1:16. Model je kombinovatelný s traktory řady 2000 a 3000 a je vhodný pro děti od 4 let. Výrobek obsahuje jeden balík a pochází z Německa.

• Detailně zpracovaný model značky Bruder
• Kombinovatelný se všemi traktory řady 2000 a 3000
• Vhodný pro děti již od 4 let
• Kvalitní německý plastový materiál

Objev podobné jako Bruder 2032 Balíkovač s baličkou John Deere

Model traktoru John Deere 5115M v měřítku 1:16 od značky Bruder nabízí realistické detaily a funkce. Hračka obsahuje posuvnou střechu, otevíratelnou kapotu motoru, odnímatelné čelní závaží a říditelnou přední nápravu. Je kompatibilní s příslušenstvím jako čelní nakladače a figurkami Bworld.

• Detailně zpracovaný model v měřítku 1:16 s vysokou funkčností
• Možnost ovládání přes střešní otvor s prodlouženým volantem
• Kombinovatelnost s příslušenstvím (nakladače, valníky) a figurkami Bworld
• Robustní konstrukce z ABS plastu vhodná pro děti od 3 let

Objev podobné jako Bruder 2106 Traktor John Deere 5115M

Traktor John Deere 7R 350 je detailně zpracovaný model v měřítku 1:16 z vysoce kvalitního ABS plastu. Disponuje řiditelnou přední nápravou, otevíratelnou kapotou motoru a dveřmi, standardním závěsným zařízením a možností připojení příslušenství. Je vhodný pro děti od 3 let a kombinovatelný s figurkami Bworld.

• Vysoce kvalitní ABS plast s lesklým povrchem bez otřepů a přetoků
• Řiditelná přední off-road náprava a otevíratelná kapota motoru i dveře
• Možnost připojení nakladačů, valníků a kombinace s figurkami Bworld
• Ovládání pomocí volantu nebo prodlouženého volantu přes střešní otvor

Objev podobné jako Bruder 3150 John Deere 7R 350

Přívěs balíkovač slámy Bruder 02017 je detailní model v měřítku 1:16. Vyroben je z plastu německou firmou Bruder a obsahuje funkční sklopnou rampu. Model je určen pro děti od 3 let a lze jej připojit k traktorům John Deere.

• Detailně zpracovaný model v měřítku 1:16
• Funkční sklopná zadní rampa pro manipulaci s balíky
• Vyrobeno z kvalitního plastu v Německu
• Kompatibilní s traktory John Deere (prodává se samostatně)

Objev podobné jako Bruder 02017 Balíkovač slámy John Deere

Selected as the Michigan Council of Teachers of Mathematics winter book club book! Rich tasks, collaborative work, number talks, problem-based learning, direct instruction…with so many possible approaches, how do we know which ones work the best? In Visible Learning for Mathematics, six acclaimed educators assert it’s not about which one—it’s about when—and show you how to design high-impact instruction so all students demonstrate more than a year’s worth of mathematics learning for a year spent in school. That’s a high bar, but with the amazing K-12 framework here, you choose the right approach at the right time, depending upon where learners are within three phases of learning: surface, deep, and transfer. This results in "visible" learning because the effect is tangible. The framework is forged out of current research in mathematics combined with John Hattie’s synthesis of more than 15 years of education research involving 300 million students. Chapter by chapter, and equipped with video clips, planning tools, rubrics, and templates, you get the inside track on which instructional strategies to use at each phase of the learning cycle: Surface learning phase: When—through carefully constructed experiences—students explore new concepts and make connections to procedural skills and vocabulary that give shape ... Unknown localization key: "more"

Objev podobné jako Visible Learning for Mathematics, Grades K-12 - Douglas Fisher, Nancy Frey, John Hattie, Sara Delano Moore, Linda M. Gojak, William Mellman

A practical introduction to the engineering science and mathematics required for engineering study and practice.Science and Mathematics for Engineering is an introductory textbook that assumes no prior background in engineering. This new edition covers the fundamental scientific knowledge that all trainee engineers must acquire in order to pass their examinations and has been brought fully in line with the compulsory science and mathematics units in the new engineering course specifications. A new chapter covers present and future ways of generating electricity, an important topic.John Bird focuses upon engineering examples, enabling students to develop a sound understanding of engineering systems in terms of the basic laws and principles. This book includes over 580 worked examples, 1300 further problems, 425 multiple choice questions (with answers), and contains sections covering the mathematics that students will require within their engineering studies, mechanical applications, electrical applications and engineering systems.This book is supported by a companion website of materials that can be found at www.routledge/cw/bird. This resource includes fully worked solutions of all the further problems for students to access, and the full solutions and marking schemes for the revision tests found within the book for instructor use. In addition, all 447 illustrations will be available ... Unknown localization key: "more"

Objev podobné jako Science and Mathematics for Engineering - John Bird

If you know a little bit about financial mathematics but don’t yet know a lot about programming, then C++ for Financial Mathematics is for you.C++ is an essential skill for many jobs in quantitative finance, but learning it can be a daunting prospect. This book gathers together everything you need to know to price derivatives in C++ without unnecessary complexities or technicalities. It leads the reader step-by-step from programming novice to writing a sophisticated and flexible financial mathematics library. At every step, each new idea is motivated and illustrated with concrete financial examples.As employers understand, there is more to programming than knowing a computer language. As well as covering the core language features of C++, this book teaches the skills needed to write truly high quality software. These include topics such as unit tests, debugging, design patterns and data structures. The book teaches everything you need to know to solve realistic financial problems in C++. It can be used for self-study or as a textbook for an advanced undergraduate or master’s level course.

Objev podobné jako C++ for Financial Mathematics - Armstrong John

For courses in teaching math methods (preK-8). Guide teachers to help all PreK to 8th grade learners make sense of math Elementary and Middle School Mathematics illustrates how children in PreK to 8th grade learn math, and then supplies concrete, effective methods of teaching math using problem-based activities. Examples of real student work, common challenges, and hundreds of classroom-ready hands-on tasks help readers visualize developmentally appropriate mathematics instruction and assessment that supports and challenges all learners. The 11th Edition, Global Edition, reflects the Common Core State Standards and NCTM''s Principles to Actions, as well as current research and the latest teaching technology. Hallmark features of this title Samples of real student work show children''s mathematical reasoning in context. Adaptations to Challenge and Support Students offer practical strategies to make activities accessible to all students. Formative Assessment Notes help educators evaluate students'' understanding of content areas and offer the best methods to assist struggling students. Common Challenges tables outline a student challenge and what it looks like, with tips on how to help. Big Ideas lists help readers envision how to form their lesson plans around major themes rather than isolated skills or concepts. Research-based strategies, NCTM Teaching Standards, and Standards ... Unknown localization key: "more"

Objev podobné jako Elementary and Middle School Mathematics: Teaching Developmentally, Global Edition - Jennifer Bay-Williams, Karen Karp, John Walle

The mom's guide to finding happiness, hope, fulfillment, and self-love as an empty nester For moms everywhere, Life After Kids: Rediscover Yourself and Thrive Beyond Motherhood is an essential guide to becoming an empty nester. When your child leaves home for new opportunities, it's hard to adjust to their absence. This book provides a roadmap to navigating this transitional life stage, filled with wisdom on finding new opportunities, focusing on developing your emotional and mental health, managing feelings of anxiety, loneliness, and uncertainty, and preparing to welcome a new phase of parenting as kids grow older and more independent. Written by Brooke Stillwell and Lynne Mouw, two health and wellness experts with decades of experience helping women maximize their potential and find fulfillment, this book helps readers understand concepts like: Why continuing to pour even more of your heart and soul into your grown kids' lives is often a step backwardsWhy women thrive as empty nesters through building emotional resilience: letting go of things you cannot control, and instead focusing on things you can controlWhy finding more purpose, rather than accumulating material possessions or indulging in leisurely activities and pastimes, is the only real way forward For all mothers looking ... Unknown localization key: "more"

Objev podobné jako Life After Kids - Brooke Stillwell, Lynne Mouw

Teach your students to become decision makers who rely on their own mathematical thinking. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes:  "Seven Significant Strategies" to teach to students as they work toward procedural fluency.  Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.

Objev podobné jako Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8 - John J. SanGiovanni, Jennifer M. Bay-Williams

Gain essential mathematical skills for machine trades and manufacturing with Peterson/McGarry/Smith’s MATHEMATICS FOR MACHINE TECHNOLOGY, Cengage International Edition, 9th Edition. This comprehensive book seamlessly connects math concepts to practical machine applications, featuring industry-specific examples, realistic illustrations and actual machine functions. From general math to trigonometry, solid geometry and introductory G- and M-codes for CNC programming, this book prepares you for success in the fields of machine trades and manufacturing. Strengthen your mathematical abilities and unlock your potential for a rewarding career.

Objev podobné jako Mathematics for Machine Technology, Cengage International Edition - Dr Kathleen McGarry, John ) Peterson, Robert ) Smith

This title is endorsed by Cambridge Assessment International Education.Written by expert authors with an international focus, this book fully covers the Cambridge O Level Mathematics syllabus (4024) for examination from 2025. It enables learners to effectively master and find connections between mathematical topics and their practical applications.- Chapters and topics are introduced through clear explanations and notes on prior knowledge needed, with worked examples that are accessible for students studying in a second language.- Key points at the end of each chapter provide opportunity for reflection to ensure that understanding and skills have been developed before students move on.- Formative exercises support active, engaged learning throughout, and aid retention of knowledge with questions that progress in difficulty to test understanding at all levels.- Regular review exercises, including past paper questions, consolidate learning and help students to prepare for assessment.- ''Non-calculator'' questions are clearly flagged so students can feel confident when approaching this type of question in their final examinations.- Numerical answers to all questions are available free on www.hoddereducation.com/cambridgeextras- Worked solutions for the review exercises are available in the Boost eBook: Teacher edition.- An editable three-year scheme of work and weekly planner is available free on www.hoddereducation.com/cambridgeextras

Objev podobné jako Cambridge O Level Mathematics Second edition - Brian Seager, Michael Handbury, John Jeskins, Jean Matthews, Heather West

Stand out, showcase your ability and succeed in your university admissions test. Whether you''re taking STEP, MAT or TMUA, this essential guide reveals tried-and-tested strategies for building the problem-solving skills you need to secure a high score.Containing expert advice and worked examples, followed by multiple-choice and extended questions that replicate the exams, this guide is designed to improve your understanding of the admissions tests and help to build the skills universities are looking for.- Learn to think like a university student - detailed guidance, thought-provoking questions and worked solutions show you how to advance your mathematical thinking- Improve your mathematical reasoning - practise the problem-solving skills you need with ''Try it out'' activities throughout the book and end-of-chapter exercises to track progress- Build a path through every problem - our authors guide you through each type of problem so that you can approach questions confidently, think on the spot and apply your knowledge to new contexts- Maximise marks and make the most of the time you have - at the end of each chapter, our authors give advice on how to tackle questions in the most time-efficient way and help you to figure out which ones will show off your ... Unknown localization key: "more"

Objev podobné jako STEP, MAT, TMUA: Skills for success in University Admissions Tests for Mathematics - David Bedford, Richard Lissaman, Tim Honeywill, Phil Chaffe

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the sixth-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the ... Unknown localization key: "more"

Objev podobné jako Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 6 - Cathy Williams, Jo Boaler, Jen Munson

Engage students in mathematics using growth mindset techniques The most challenging parts of teaching mathematics are engaging students and helping them understand the connections between mathematics concepts. In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the first-grade level through visualization, play, and investigation. During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message—that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that: There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the ... Unknown localization key: "more"

Objev podobné jako Mindset Mathematics: Visualizing and Investigating Big Ideas, Grade 1 - Cathy Williams, Jo Boaler, Jen Munson

For more than two thousand years a familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today, unfortunately, the traditional place of mathematics in education is in grave danger. The teaching and learning of mathematics has degenerated into the realm of rote memorization, the outcome of which leads to satisfactory formal ability but does not lead to real understanding or to greater intellectual independence. This new edition of Richard Courant''s and Herbert Robbins''s classic work seeks to address this problem. Its goal is to put the meaning back into mathematics. Written for beginners and scholars, for students and teachers, for philosophers and engineers, What is Mathematics?, Second Edition is a sparkling collection of mathematical gems that offers an entertaining and accessible portrait of the mathematical world. Covering everything from natural numbers and the number system to geometrical constructions and projective geometry, from topology and calculus to matters of principle and the Continuum Hypothesis, this fascinating survey allows readers to delve into mathematics as an organic whole rather than an empty drill in problem solving. With chapters largely independent of one another and sections that lead upward from basic to more advanced ... Unknown localization key: "more"

Objev podobné jako What Is Mathematics? - Herbert Robbins, Richard, 1888-1972 Courant

Exam Board: IBLevel: MYPSubject: MathematicsFirst Teaching: September 2016First Exam: June 2017A concept-driven and assessment-focused approach to Mathematics teaching and learning.- Approaches each chapter with statements of inquiry framed by key and related concepts, set in a global context- Supports every aspect of assessment using tasks designed by an experienced MYP educator- Differentiates and extends learning with research projects and interdisciplinary opportunities- Applies global contexts in meaningful ways to offer an MYP Mathematics programme with an internationally-minded perspectiveRita Bateson was, until very recently, the Curriculum Manager for MYP Mathematics and Sciences at the International Baccalaureate® (IB) and continues to be involved in curriculum review. She is an experienced teacher of MYP and DP Mathematics and Sciences, and is Head of Mathematics in her current school. She has taught in many international schools in Europe as well as North America. Her interest include overcoming mathematics anxiety in pupils and STEM education. She is also the author of MYP by Concept 4&5 Mathematics. Irina Amlin has been an MYP Mathematics educator and department head, the Chair and frequent presenter of the island-wide Bermuda Math Educators'' Learning Network, and has been involved in IB curriculum development and assessment activities. Her primary area of focus ... Unknown localization key: "more"

Objev podobné jako Mathematics for the IB MYP 1 - Irina Amlin, Rita Bateson

This volume, originally published in China and translated into four other languages, presents a fascinating and unique account of the history of mathematics, divided into eight chronologically organized chapters. Tracing the development of mathematics across disparate regions and peoples, with particular emphasis on the relationship between mathematics and civilization, it examines mathematical sources and inspirations leading from Egypt, Babylon and ancient Greece and expanding to include Chinese, Indian and Arabic mathematics, the European Renaissance and the French revolution up through the Nineteenth and Twentieth Centuries. Each chapter explores connections among mathematics and cultural elements of the time and place treated, accompanying the reader in a varied and exciting journey through human civilizations. The book contemplates the intersections of mathematics with other disciplines, including the relationship between modern mathematics and modern art, and the resultingapplications, with the aid of images and photographs, often taken by the author, which further enhance the enjoyment for the reader. Written for a general audience, this book will be of interest to anyone who''s studied mathematics in university or even high school, while also benefiting researchers in mathematics and the humanities.Â

Objev podobné jako A Brief History of Mathematics - Tianxin Cai

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics This book covers all the content needed for the Edexcel AS level Pure Mathematics exam. It can also be used alongside the Year 2 book to cover all the content needed for the Edexcel A level Pure Mathematics exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Mathematics Pure Mathematics Year 1/AS Textbook + e-book - Alistair Macpherson, Su Nicholson, Robert Ward-Penny, Keith

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the compulsory Edexcel AS level Core Pure Mathematics exam. It can also be used alongside Book 2 to cover all the content needed for the compulsory Edexcel A level Core Pure Mathematics exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Core Pure Mathematics Book 1/AS Textbook + e-book matches the Pearson Edexcel exam structure and is fully ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Further Mathematics Core Pure Mathematics Book 1/AS Textbook + e-book - Alistair Macpherson, Su Nicholson, Keith Pledge

This book provides in-depth coverage of Probability & Statistics 1 for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study.Exam Board: Cambridge Assessment International EducationFirst teaching: 2018 First examination: 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 and examination from 2020. This title is endorsed by Cambridge Assessment International Education.Written by expert authors, this Student Book:• covers the complete content of Probability & Statistics 1 with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus• sets mathematics in real-world contexts that emphasise practical applications and career paths, with inspiring case studies and discussion activities that showcase how mathematics is relevant to different roles• develops the key A Level mathematical skills of mathematical modelling, problem-solving and communication through dedicated questions and teaching• helps you master mathematics ... Unknown localization key: "more"

Objev podobné jako Cambridge International AS & A Level Mathematics Probability and Statistics 1 Student’s Book - Jonny Griffiths, Yimeng Gu, Louise Ackroyd

A crystal-clear and practical blueprint to software disassembly x86 Software Reverse-Engineering, Cracking, and Counter-Measures is centered around the world of disassembling software. It will start with the basics of the x86 assembly language, and progress to how that knowledge empowers you to reverse-engineer and circumvent software protections. No knowledge of assembly, reverse engineering, or software cracking is required. The book begins with a bootcamp on x86, learning how to read, write, and build in the assembly that powers a massive amount of the world’s computers. Then the book will shift to reverse engineering applications using a handful of industry favorites such as IDA, Ghidra, Olly, and more. Next, we move to cracking with techniques such as patching and key generation, all harnessing the power of assembly and reverse engineering. Lastly, we’ll examine cracking from a defensive perspective. Providing learners with techniques to be a better defender of their own software, or knowledge to crack these techniques more effectively. Assembly: computer Architecture, x86, system calls, building and linking, ASCII, condition codes, GDB, control flow, stack, calling conventionsReverse Engineering: reconnaissance, strings, RE strategy, stripping, linking, optimizations, compilers, industry toolsCracking: patching, key checkers, key generators, resource hacking, dependency walkingDefense: anti-debugging, anti-tamper, packing, cryptors/decryptors, ... Unknown localization key: "more"

Objev podobné jako x86 Software Reverse-Engineering, Cracking, and Counter-Measures - Christopher Domas, Stephanie Domas

Study smarter and stay on top of your discrete mathematics course with the bestselling Schaum’s Outline—now with the NEW Schaum’s app and website! Schaum’s Outline of Discrete Mathematics, Fourth Edition is the go-to study guide for more than 115,000 math majors and first- and second-year university students taking basic computer science courses. With an outline format that facilitates quick and easy review, Schaum’s Outline of Discrete Mathematics, Fourth Edition helps you understand basic concepts and get the extra practice you need to excel in these courses.Coverage includes set theory; relations; functions and algorithms; logic and propositional calculus; techniques of counting; advanced counting techniques, recursion; probability; graph theory; directed graphs; binary trees; properties of the integers; languages, automata, machines; finite state machines and Turning machines; ordered sets and lattices, and Boolean algebra.Features • NEW to this edition: the new Schaum’s app and website!• NEW to this edition: 20 NEW problem-solving videos online• 467 solved problems, and hundreds of additional practice problems• Outline format to provide a concise guide to the standard college course in discrete mathematics• Clear, concise explanations of discrete mathematics concepts• Expanded coverage of logic, the rules of inference and basic types of proofs in mathematical reasoning• Increased emphasis ... Unknown localization key: "more"

Objev podobné jako Schaum's Outline of Discrete Mathematics, Fourth Edition - Marc Lipson, Seymour Lipschutz

For first-year undergraduate modules in Engineering Mathematics. Develop understanding and maths skills within an engineering context Modern Engineering Mathematics, 6th Edition by Professors Glyn James and Phil Dyke, draws on the teaching experience and knowledge of three co-authors, Matthew Craven, John Searl and Yinghui Wei, to provide a comprehensive course textbook explaining the mathematics required for studying first-year engineering. No matter which field of engineering you will go on to study, this text provides a grounding of core mathematical concepts illustrated with a range of engineering applications. Its other hallmark features include its clear explanations and writing style, and the inclusion of hundreds of fully worked examples and exercises which demonstrate the methods and uses of mathematics in the real world. Woven into the text throughout, the authors put concepts into an engineering context, showing you the relevance of mathematical techniques and helping you to gain a fuller appreciation of how to apply them in your studies and future career. Also available with MyLab Math MyLabâ„¢ is the teaching and learning platform that empowers you to reach every student. By combining trusted author content with digital tools and a flexible platform, MyLab personalizes the learning experience and improves results for ... Unknown localization key: "more"

Objev podobné jako Modern Engineering Mathematics - Glyn James, Phil Dyke

This book provides in-depth coverage of Mechanics for Cambridge International AS and A Level Mathematics 9709, for examination from 2020 onwards. With a clear focus on mathematics in life and work, this text builds the key mathematical skills and knowledge that will open up a wide range of careers and further study.Exam Board: Cambridge Assessment International EducationFirst teaching: 2018 First examination: 2020This student book is part of a series of nine books covering the complete syllabus for Cambridge International AS and A Level Mathematics (9709) and Further Mathematics (9231), for first teaching from September 2018 and first examination from 2020. This title is endorsed by Cambridge Assessment International Education.Written by expert authors, this Student Book:• covers the complete content of Mechanics (formerly Mechanics 1) with clear references to what you will learn at the start of each chapter, and coverage that clearly and directly matches the Cambridge syllabus• sets mathematics in real-world contexts that emphasise practical applications and career paths, with inspiring case studies and discussion activities that showcase how mathematics is relevant to different roles• develops the key A Level mathematical skills of mathematical modelling, problem-solving and communication through dedicated questions and teaching• helps you master mathematics with varied ... Unknown localization key: "more"

Objev podobné jako Cambridge International AS & A Level Mathematics Mechanics Student’s Book - Michael Kent, Tom Andrews

Written by an experienced teacher and teacher educator with widespread experience of teaching mathematics in the UK and internationally, the bestselling Understanding and Teaching Primary Mathematics combines pedagogy and subject knowledge to build confidence and equip you with all the skills and know-how you need to successfully teach mathematics to children of any age.This fifth edition has been completely updated to include the latest developments in learning and teaching mathematics, including mastery approaches, a Singapore approach and the use of manipulatives in the primary classroom. There are new activities for you to use in your teaching and links to the dedicated website, which contains materials to develop a personal portfolio, more activities to use in your classroom and presentations and podcasts to support your further professional development to reflect the latest research developments. It covers all areas of the mathematics curriculum and will allow you to become a confident teacher of mathematics through developing your own subject knowledge.Tony draws on his many years of experience teaching mathematics and working with early career teachers to share classroom activities which will support you in learning mathematics through engaging in mathematical activity with your learners.

Objev podobné jako Understanding and Teaching Primary Mathematics - Tony Cotton

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics This book can be used alongside the Year 1 book to cover all the content needed for the Edexcel A level Pure Mathematics exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel A level Mathematics Pure Mathematics Year 2 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel A level Mathematics Pure Mathematics Year 2 Textbook + e-book - Alistair Macpherson, Keith Pledger, Jack Barraclough, Ian Bettison, Ha

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book can be used alongside the Year 1 book to cover all the content needed for the compulsory Edexcel A level Core Pure Mathematics exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel A level Further Mathematics Core Pure Mathematics Book 2 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s interactive scheme of work. All of the books in this series focus on ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel A level Further Mathematics Core Pure Mathematics Book 2 Textbook + e-book

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. Our A level Mathematics Pure Year 2 Practice Book helps you get exam-ready with confidence and practice at the right pace. Coverage: the practice workbooks cover all Pure, Statistics and Mechanics topics Quantity: the most A level question practice available, with over 2,000 extra questions per book Practice at the right pace: start with the essentials, build your skills with various practice questions to make connections between topics, then apply this to exam-style questions at the end of each chapter Get exam-ready with confidence: differentiated questions including ‘Bronze, Silver, Gold'' in each chapter, and a mixed problem-solving section for each book, will guide and help you to develop the skills you need for your exams Designed to be used flexibly, the practice books are fully mapped to the scheme of work and textbooks so you can use them seamlessly in and out of the classroom and all year round. Use them lesson by lesson, topic by topic, for homework, revision ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Mathematics Pure Mathematics Year 2 Practice Book

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Further Pure Mathematics 1 exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Further Pure Mathematics 1 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Further Mathematics Further Pure Mathematics 1 Textbook + e-book

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Decision Mathematics 1 exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Decision Mathematics 1 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well as supporting ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Further Mathematics Decision Mathematics 1 Textbook + e-book

Mathematics of Tabletop Games provides a bridge between mathematics and hobby tabletop gaming. Instead of focusing on games mathematicians play, such as nim and chomp, this book starts with the tabletop games played by avid gamers and hopes to address the question: which field of mathematics concerns itself with this situation?Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics.Features Presents an entry-level exposition of interesting mathematical concepts that are not commonly taught outside of upper-level mathematics courses Acts as a resource for mathematics instructors who wish to provide new examples of standard mathematical concepts Features material that may help game designers and developers make design decisions about game mechanisms Provides working Python code that can be used to solve common questions about gamesCovers a broad range of mathematical topics that could be used as survey material for undergraduates curious about mathematics.

Objev podobné jako Mathematics of Tabletop Games - Aaron Montgomery

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Decision Mathematics 2 exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Decision Mathematics 2 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well as supporting ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Further Mathematics Decision Mathematics 2 Textbook + e-book

The UK''s most trusted A level Mathematics resources With over 900,000 copies sold (plus 1.3 million copies sold of the previous edition), Pearson''s own resources for Pearson Edexcel are the market-leading and most trusted for AS and A level Mathematics. This book covers all the content needed for the optional Edexcel AS and A level Further Pure Mathematics 2 exams Enhanced focus on problem-solving and modelling, as well as supporting the large data set and calculators Packed with worked examples with guidance, lots of exam-style questions, practice papers, and plenty of mixed and review exercises Full worked solutions to every question available free and online for quick and easy access. Plus free additional online content with GeoGebra interactives and Casio calculator tutorials Practice books also available offering the most comprehensive and flexible AS/A level Maths practice with over 2000 extra questions Includes access to an online digital edition (valid for 3 years once activated) Pearson Edexcel AS and A level Further Mathematics Further Pure Mathematics 2 Textbook + e-book matches the Pearson Edexcel exam structure and is fully integrated with Pearson Edexcel''s interactive scheme of work. All of the books in this series focus on problem-solving and modelling, as well ... Unknown localization key: "more"

Objev podobné jako Pearson Edexcel AS and A level Further Mathematics Further Pure Mathematics 2 Textbook + e-book

A captivating book that takes you on a journey through the world of reverse colouring that will unleash your creativity and allow your imagination to soar. The book has the colors, you draw the lines. Immerse yourself in hours of fun and creativity with the mesmerizing world of reverse colouring. This unique artistic activity combines the meditative qualities of colouring, the cognitive stimulation of puzzles, and the freedom to express your creativity. Each page invites you to slow down, let go and allow your pen to wander freely, finding its way on the page. With a watercolour image as the background, all you need is a pen as you trace shapes, draw patterns, shade, or even cover areas with dots. This simple, deeply satisfying meditative activity will calm your mind while strengthening your artistic self-confidence. The author takes you on a stroll through lush and flowery landscapes, inviting you to imagine what happens next as you set the rules and create your own magical atmosphere. You can be realistic, have a vision or set your imagination free as if you were gazing at clouds in the sky. With 50 original works of art printed on special drawing paper, you have ... Unknown localization key: "more"

Objev podobné jako Reverse Coloring Book: Drawing Nature with Inverse Coloring - Cecile Baude-Tagnard

Solidly grounded in up-to-date research, theory, and technology, Teaching Secondary Mathematics is a practical, student-friendly, and popular text for secondary mathematics methods courses. It provides clear and useful approaches for mathematics teachers and shows how concepts typically found in a secondary mathematics curriculum can be taught in a positive and encouraging way. The thoroughly revised fifth edition combines this pragmatic approach with truly innovative and integrated technology content throughout. Synthesized content between the book and a comprehensive Instructor and Student Resource website offers expanded discussion of chapter topics, additional examples, and technological tips, such as using and assessing artificial intelligence.Each chapter features tried-and-tested pedagogical techniques, problem-solving challenges, discussion points, activities, mathematical challenges, and student-life-based applications that will encourage students to think and do.New to the fifth edition:A fully revised chapter on technological advancements in the teaching of mathematics, including the use of artificial intelligenceA new chapter on equity, shame, and anxiety in the mathematics classroomConnections to both the updated National Council of Teachers of Mathematics (NCTM) Focal Points and StandardsProblem-solving challenges and sticky questions featured in each chapter to encourage students to think through everyday issues and possible solutionsA fresh interior design to better highlight pedagogical elements and key featuresA ... Unknown localization key: "more"

Objev podobné jako Teaching Secondary Mathematics - David Rock, Thomas J. P. Brady, Douglas K. Brumbaugh

Korres White Pine Meno-Reverse™, 40 ml, Pleťové krémy pro ženy, Péče, která rozumí potřebám zralé pleti Denní hydratační krém proti stárnutí pleti Korres White Pine Meno-Reverse™ je skvělou volbou pro suchou až velmi suchou postmenopauzální pleť. S patentovaným extraktem z bílé borovice a technologií Meno-Reverse™ navrací pleti hydrataci, pevnost a mladistvý vzhled. Přineste své pleti komfort a výživu, kterou si zaslouží, a objevte sílu přírodního složení inspirovaného moudrostí přírody. Vlastnosti: intenzivně hydratuje a zjemňuje suchou pleť navrací pružnost zralé pleti dodává pleti ultra výživu redukuje viditelnost hlubokých vrásek zlepšuje celkový vzhled a strukturu pleti Výsledky testování: → test sebehodnocení in vivo, 32 žen, věk 55–70 let 8 z 10 žen potvrdilo, že svou pleť vnímaly jako před menopauzou již za 4 týdny méně hlubokých vrásek a skvrn měkčí, vyživená pleť a příjemný pocit po celý den při první aplikaci Složení: patentovaný extrakt z bílé borovice technologie Meno-Reverse™ – zaměřuje se na specifické potřeby postmenopauzální pleti obsahuje 94,5 % složek přírodního původu Jak aplikovat: Krém White Pine Meno-Reverse™ naneste na čistý obličej a krk, vyhněte se oblasti očí. Používejte každé ráno po aplikaci svého oblíbeného séra.

Objev podobné jako Korres White Pine Meno-Reverse™ denní hydratační krém proti stárnutí pleti 40 ml