Copyright 2025
Paperback
Hardback
ISBN 9781041013136
244 Pages 53 B/W Illustrations
June 23, 2025 by Chapman & Hall
How do we conquer uncertainty, insecurity, and anxiety over college mathematics? You can do it, and this book can help.
The author provides various techniques, learning options, and pathways. Students can overcome the barriers that thwart success in mathematics when they prepare for a positive start in college and lay the foundation for success.
Based on interviews with over 50 students, the book develops approaches to address the struggles and success these students shared. Then the author took these ideas and experiences and built a process for overcoming and achieving when studying not only the mathematics many colleges and universities require as a minimum for graduation, but more to encourage reluctant students to look forward to their mathematics courses and even learn to embrace additional ones.
Success breeds interest, and interest breeds success. Math anxiety is based on test anxiety. The book provides proven strategies for conquering test anxiety. It will help find ways to interest students in succeeding in mathematics and assist instructors on pathways to promote student interest, while helping them to overcome the psychological barriers they face. Finally, the author shares how math is employed in the “real world,” examining how both STEM and non- STEM students can employ math in their lives and careers. Ultimately, both students and teachers of mathematics will better understand and appreciate the difficulties and how to attack these difficulties to achieve success in college mathematics.
1 Why do I Hate Math?
What is Math Anxiety?
Why Should I Listen to This Guy?
Did You Have a Math Bully?
Loss of Control and the Fear of Feeling Stupid
Math Feels Like a Poor Fit
Math is Viewed as Authoritative
Ambiguity Should be a Four- Letter Word
Math is Required for Every Degree. Who Did This to Us?
Returning to School After Some Time Away?
Are Men "Better at Math" Than Women?
Addressing Racial Inequalities in Math
Overcoming Defeatist Attitudes
The Development and Treatment of Math Anxiety is a Process
Why in the World? Part 1
Why in the World Does Multiplying a Number by Zero
Give Us Zero?
Activity
2 I’m So Confused….Navigating the Math System
First Things First
Choosing a School
Community Colleges
Four- Year Colleges
Online Institutions
Financial Aid and Scholarships
The Placement Test
What is Developmental Math, and Will I Have to Take It?
What is "College- Level Math?"
The Traditional Pathway
Alternative Math Pathways
Quantitative Reasoning (or Math for the Non- Math Major)
Introduction to Statistics
Teacher Preparatory Classes
What are Corequisites?
The STEM Pathway
Undecided?
Modality Types
Traditional Classes
The Emporium Model
Online
Virtual Learning
Inquiry or Group- Based Instruction
What is Your Learning Style?
Learning Style Quiz
Why in the World? Part 2
Why in the World is a Number Divided by Zero "Undefined?"
Activity
3 How Do I Prepare for College and Math?
Register as Early as Possible and Do Your Homework
Choosing a Professor
The Biggest Reason for Failure in Math and Something that May
Surprise You!
Being Behind May Not be Your Fault
Preparing for Your Math Class Even Before the First Day
Statistics Can be Deceiving
What if I Struggle with Basic Arithmetic?
How is Your Number Sense?
Developing a Sense of Community and Belonging
My Own Story in Developing a Sense of Community
The Challenges of Meeting People
Ensuring You Have Your Materials
Disability Services (If Needed)
Are Your Basic Needs Being Met?
Figure Out Your Math Time!
A Fresh Start
Why in the World? Part 3
Why in the World Doesn’t "PEMDAS" Always Work?
Activity
4 Getting Off and Staying On the Right Foot
What is Your Math Personality?
The First Day
Technology in Math
Calculators
Interactive Math Software
Zoom Meetings
I’m in My Nightmare! I’m Lost in Class!
Does Reading a Math Textbook Help?
What Can You do Outside of Class to Help?
Become a Regular at the Tutorial Center
Study Groups
Online Resources and Artificial Intelligence
What Happens When Life Happens?
I Understood What We Were Doing in Class, But I Drew a Blank
When I Tried It at Home
Math Vocabulary: Yes, that Sounds Awful!
Suggestions for Each Learning Style
Tips for the Auditory Learner
Tips for the Visual Learner
Tips for the Kinesthetic/ Tactile Learner
Back to the Quantitative and Qualitative Thinkers
Why in the World? Part 4
Practice Some Math
Activity and Math Exercises
5 I Hate, Hate, Hate These Math Topics!
Fractions
Why Do Students Hate Fractions?
Where Will I Need Fractions?
What Can We Do About Fractions?
What Should I Know about Fractions? And Some
Tips to Get Started
A Look at Adding and Subtracting Fractions
How Does This Apply to Higher- Level Math?
A Look at Multiplication and Division of Fractions
How Does this Apply to Higher- level Math?
Where Do Students Get Stuck with Fractions?
The Laws of Exponents
What is an Exponent?
Why do Students Hate Exponents?
What are the Laws of Exponents?
Wait? What?
Of Course it Gets More Complicated!
What About Negative Exponents? Do They Exist?
Where Will I See the Laws of Exponents?
Exponents can be Weird?
Probability
Why is Probability Hated?
When Will I Need Probability for College Math?
Do I Need to Prepare for Probability in Advance?
Geometry: Angles, Lines and Rays…Oh My!
Why is This Topic so Bad?
Where is Geometry Used in College- Level Math Classes?
Do I Need to Prepare for Angles, Lines, Rays, etc.?
Factoring
Why do Students Hate Factoring?
Why Does Factoring Exist and When Will I Need it?
So, Let’s Factor!
First Type of Factoring
Second Type of Factoring
Slope of a Line
Where is Slope Used?
Why do Students Hate Slope?
Slope has a Formula
Another Way to Determine Slope
Should I Prepare for Slope?
Why in the World? Part 5
Why in the World is Anything Raised to the Zero
Power Always 1?
Practice Problems
Practice with Fractions. Be sure to Reduce the Fractions
Geometry: Angles, Lines, and Rays
Factoring
Slope
Activity
6 Word Problems: The Bane of My Existence
Why do Word Problems Bring Out the Anxiety?
Reading Comprehension or Reading Differences
Not Even Knowing Where to Start
Math Terminology is an Issue
Quantitative Personalities may Struggle
Lacking the Prerequisite Skills
Bad Experiences Lead to a Self- Fulfilling Prophecy
What are the Prerequisite Skills Needed?
Now, Attack the Problem!
Example 1
Read the Problem
Ask Yourself some Questions
Understand the Prerequisites
Identify What You are Solving For and Translate
Solve the Problem
Does this Answer Make Sense?
Example 2
Read the Problem
Ask Yourself Some Questions
Understanding the Prerequisites
Identify What You are Solving For and Translate
Solve the Problem
Does this Answer Make Sense?
Example 3
Read the Problem
Understand the Prerequisites
Before Translating, Draw a Picture or Diagram (Sometimes)
Identify and Translate
Solve the Problem
Does the Answer Make Sense?
Mutual Exclusivity
Example 4
Understand the Prerequisites
Before Translating, Draw a Picture or Diagram (Sometimes)
Identify and Translate
Solve the Problem
Does the Answer Make Sense?
Example 5
Read the Problem
Ask Yourself Some Questions
Understand the Prerequisites
Identify and Translate
Solve the Problem
Does the Answer Make Sense?
Example 6
Read the Problem
Ask Yourself Some Questions
Understand the Prerequisites
Identify, Translate, and Draw a Picture
Solve the Problem
Does the Answer Make Sense?
Struggling?
Look Over your Class Notes
Is There an Online Tutorial?
Ask your Instructor….Right Away!
It Works!
Why in the World? Part 6
Why in the World do we Flip the Sign in an Inequality When
Dividing by a Negative Coefficient?
Exercises to Help You Practice
Basic Algebra Word Problems
More Advanced Algebraic Word Problems
Some Basic Probability
Activity
7 Tackling Exams
Test Anxiety? You are in Good Company
Root Causes of Test Anxiety
Poor Test History
Fear of Failure
High- Stakes Exams
Poor Test Preparation
Tackling an Exam Starts Long Before the Exam
Positive Thoughts
How do I Study for a Math Exam?
Is There a Study Guide?
Clean up any Mistakes
Data Drop Off (Memory Dump
Timed Tests!
The Day of the Exam
Try to Get Enough Sleep
Eat Well During the Day
Try to Stay in a Good Mood
Online Test- Takers
You Get the Test!
Now, Use the Data Drop Off (Memory Dump)
Start Where You Feel Most Comfortable!
Seemingly Contradictory Advice
Pacing the Exam
The Waiting is the Hardest Part
Celebrate!
Why in the World? Part 7
Why in the World Can’t I just Divide Stuff to Simplify?
Activity
8 Learning From Success, Failure, and Experience
Assessing Your Exam
Check Out Your Mistakes
How About your Grade?
Use Your Exam as a Study Guide
Learning from Success
Should I Withdraw from the Class?
The Reality of Failure
My Experience with Failure
Learning from Failure
Did You Lack Prerequisite Skills?
Did You Devote Enough Time to Your Studies?
Were You in the Wrong Modality?
Do You Need to Change Your Pathway?
Did You go at it Alone?
Generic Questions
Why in the World? Part 8
Why in the World do Logarithms Exist?
Activity
9 When Will Math Help Me in My Life?
Non- STEM Students
Helping Others
Managing Money
Predicting the Cost of Living
Being a Conscientious Consumer
Computing Depreciation Costs
Statistics can do a Lot of Explaining
Higher- Level Math Classes
Trigonometry
Pre- Calculus
The Calculus Sequence
Differential Equations
Linear Algebra
Proof Writing Classes
STEM Students
High School Math Teacher
Engineer
Computer Scientist
Astronomy
Can I Survive Calculus?
Confidence
Now Go Do This!
Appendix A
Appendix B
Appendix C
Copyright 2025
Hardback
ISBN 9781032949000
272 Pages 182 B/W Illustrations
July 9, 2025 by Chapman & Hall
This book presents an opportunity to learn difference and differential equations through a modelling-first approach. The text is meant as an introduction to those equations and not as a text only for modelling courses. No previous exposure to these equations is expected. Modeling is presented as the vehicle for learning difference and differential equations.
Although the topics in difference and differential equations are consistent with those in other textbooks, this approach differs. The presentation starts with a model (or several models) and presents the solution with minor discussions. Then, methods to obtain those solutions are presented and show these same models and others again in more detail.
This approach is designed to focus on the use of difference and differential equations to solve real world problems, and to learn not only these primary topics, but how to apply these through modeling.
The authors begin with a review of matrix algebra, then an introduction to modelling. The text progresses to Discrete Dynamical Systems, and then to the standard organization of most DE texts, making the alignment with a current syllabus easier.
Technology is a significant modeling component. EXCEL, Python, and MAPLE are presented as methods to solve the models. The material has been class tested at The US Military Academy at West Point, Marion University, and William and Mary, and The Naval Postgraduate School with great success.
1. Matrix Algebra Review
2. Mathematical Modeling and Technology for Difference and Differential Equations
3. Modeling Discrete Dynamical Systems (DDS)
4. Systems of First Order Difference Equations
5. Introduction, Basic Concepts, and Techniques in Modeling First Order Ordinary Differential Equations
6. Modeling with Numerical Solutions to Differential Equations---IVP for ODEs with Technology
7. Numerical Output for Analysis: Graphical and Percent Error
8. Higher Order Differential Equations
9. Higher Order Numerical Methods to Solve IVP and BVP
10. System of Linear and Nonlinear ODEs
11. Numerical Solutions to Systems of ODES
12. Modeling using Laplace Transforms
13. Answers to Selected Exercises
Copyright 2025
Hardback
816 Pages 17 B/W Illustrations
August 1, 2025 by Chapman & Hall
ZAG Handbook of Algebraic Geometry provides an expansive collection of extended summaries of all the research talks given at the worldwide ZAG (Zoom Algebraic Geometry) Seminar as well as contributed short notes. Constructed from contributions from 2020-24 by active research algebraic geometers from all continents, the book is aimed at researchers in algebraic geometry and related fields who want to gain a comprehensive understanding of state-of-the-art research in algebraic geometry. The book is extensive and wide-ranging, and offers material suitable to multiple levels of readership: from advanced undergraduate students in mathematics to active specialised researchers.
・ A showcase of the most important worldwide trends in algebraic geometry in recent years
・ Over two hundred short summaries of state-of-the-art research in algebraic geometry accessible to other mathematicians
・ A combination of contributions by renowned mathematicians, key researchers and new talent
・ Links to recordings of hour-long presentations for each contribution.
1. Algebraic geometry in the times of Covid / Ivan Cheltsov and Jesus Martinez-Garcia
2. Models of Fano 3-folds / Hamid Abban
3. Weighted Ehrhart polynomials and series for the standard simplex / Praise Adeyemo
4. Advances in moduli theory / Jarod Alper
5. Normal form of a holomorphic Lagrangian submanifold / Ekaterina Amerik
6. Koszul modules and applications / Marian Aprodu
7. Euler characteristics of aspherical Kahler manifolds / Donu Arapura
8. Birational geometry of Calabi-Yau pairs and Cremona transformations / Carolina Araujo
9. Enumerating punctured log maps via wall-crossing / Hulya Arguz
10. Biregular and birational geometry of rational nodal quartic double solids / Artem Avilov
11. Chern character of quantizable sheaves / Vladimir Baranovsky and Victor Ginzburg
12. Vector bundles on Fano threefolds and K3 surfaces / Arnaud Beauville
13. Cylinders in Del Pezzo surfaces with Du Val singularities / Grigory Belousov
14. Approximation of differentiable submanifolds by real algebraic subvarieties / Olivier Benoist
15. Kahler-Einstein metrics, Archimedean zeta functions and phase transitions / Robert Berman
16. Geometry of 3-dimensional Del Pezzo fibrations in positive characteristic / Fabio Bernasconi
17. Geometry of polarised varieties / Caucher Birkar
18. On properness of K-moduli spaces and optimal destabilizations / Harold Blum
19. Surface with ample canonical bundle and Kuranishi space a nonreduced point / Christian Boehning
20. Projective geometry approach to the Jacobian conjecture / Alexander Borisov
21. Explicit equations of surfaces of general type / Lev Borisov /
22. General type results for moduli of hyperkahler varieties / Emma Brakkee
23. Geometric structures on spaces of quadratic differentials / Tom Bridgeland
24. Extending Tom and Jerry for Fano 3-folds / Gavin Brown, Stephen Coughlan and Tom Ducat
25. Supercycles and stable supermaps / Ugo Bruzzo and Daniel Hernandez Ruiperez
26. Arcs and singularities / Nero Budur
27. Chern?Weil theory and Hilbert?Samuel theorem for semipositive singular toroidal metrics / Jose Ignacio Burgos Gil
28. Index 2 Fano 3-folds and double covers / Livia Campo
29. Uniqueness of enhancements of triangulated categories / Alberto Canonaco, Amnon Neeman and Paolo Stellari
30. On the birational geometry of foliations / Paolo Cascini
31. Effective cones of moduli spaces of stable rational curves and blown up toric surfaces / Ana-Maria Castravet
32. Nodal surfaces, coding theory, and cubic discriminants / Fabrizio Catanese
33. The minimal model program for arithmetic surfaces enriched by a Brauer class / Daniel Chan
34. Low dimensional components in the K-moduli of smoothable Fano 3-folds / Ivan Cheltsov
35. Remarks on n-folds of type (1,n) / Jungkai Chen
36. Singularities on toric fibrations / Yifei Chen and Caucher Birkar
37. On the distribution of canonical volumes and moduli spaces of varieties of general type / Meng Chen
38. Subadditivity theorem for Okounkov bodies / Sung Rak Choi
39. Enumeration of Terracini schemes / Ciro Ciliberto
40. Numerical characterization of complex torus quotients / Benoit Claudon
41. Slope inequalities and ample cone of KSB moduli spaces / Giulio Codogni
42. The cohomology of the moduli space of sheaves on surfaces / Izzet Coskun
43. Orbifold quot schemes via the le Bruyn?Procesi theorem / Alastair Craw
44. On quadratic points on intersections of two quadrics / Brendan Creutz and Bianca Viray
45. Deformations of exterior differential ideals and applications / Fernando Cukierman
46. Log minimal model program for Kahler 3-folds / Omprokash Das
47. CSCK metrics on rank one spherical Fano fourfolds / Thibaut Delcroix
48. K-stability of P^3 blown up along the disjoint union of a twisted cubic curve and a line / Elena Denisova
49. Stability of fibrations / Ruadhai Dervan
50. Wall crossing for K-moduli spaces of plane curves / Kristin DeVleming
51. The bottleneck degree of algebraic varieties / Sandra Di Rocco
52. Dynamical filtrations| / Tien-Cuong Dinh, Hsueh-Yung Lin, Keiji Oguiso and De-Qi Zhang
53. Roth's theorem for adelic curves / Paolo Dolce and Francesco Zucconi
54. Enumerative geometry, fredholm analysis and moduli spaces of surfaces of general type Simon Donaldson
55. Bounding the complexity of 2-loop Feynman integrals / Charles Doran
56. K-stability of P^3 blown up along smooth curves of genus 4 and degree 6 / Tiago Duarte Guerreiro
57. Rigidity of affine Brieskorn-Pham threefolds / Adrien Dubouloz
58. Birational geometry and cylindricity of Severi-Brauer varieties / Adrien Dubouloz, Kento Fujita, Takashi Kishimoto and Takuzo Okada /Alexey Elagin
59. Okawa's theorem and wide subcategories of coherent sheaves on curves
60. Mixed Hodge structure decomposition of alexander modules into generalized eigenspaces / Eva Elduque
61. Local stability threshold of Del Pezzo surfaces of degree 2 / Erroxe Etxabarri Alberdi /
62. Rational simple connectedness and the quintic Del Pezzo threefold /Andrea Fanelli
63. K3 structures from singular Fano varieties / Enrico Fatighenti
64. An overview of homotopy path algebras / David Favero
65. Quasi-invariants and free arrangements / Misha Feigin
66. The Brasselet-Schurmann-Yokura conjecture on L-classes of singular varieties / Javier Fernandez de Bobadilla and Irma Pallares Torres
67. Notes on motivic integration on Berkovich spaces / Tommaso de Fernex
68. Counting sheaves by counting curves / Soheyla Feyzbakhsh and Richard Thomas
69. On the boundedness of elliptically fibered Calabi-Yau threefolds / Stefano Filipazzi
70. Connected algebraic groups acting on Fano fibrations over P^1 / Enrica Floris
71. Maximal automorphism groups of surfaces / Pascal Fong and Matilde Maccan
72. A canonical Hodge theoretic projective structure on compact Riemann surfaces / Paola Frediani
73. On extremal contractions of log canonical pairs / Osamu Fujino
74. On the singular loci of higher secant varieties of Veronese embeddings / Katsuhisa Furukawa
75. The Bourbaki degree of a plane curve / Daniel Futata and Marcos Jardim
76. Compactifications of the moduli space of marked cubic surfaces / Patricio Gallardo
77. Intrinsic mirrors for minimal adjoint orbits / Elizabeth Gasparim
78. On a generalized Batyrev’s cone conjecture / Yoshinori Gongyo
79. Complex curves in hypercomplex nilmanifolds / Iulia Gorginian
80. Projective flatness over Klt spaces and characterisation of finite quotients of projective spaces / Daniel Greb
81. Distinguishing triangle-free level-one phylogenetic networks using computational algebraic geometry / Elizabeth Gross
82. Open FJRW theory and mirror symmetry: a ZAG lecture / Mark Gross, Tyler Kelly and Ran Tessler
83. Recent progress in the MMP for 3-folds and 4-folds in char p>0 / Christopher Hacon
84. Rationality questions on Seshadri constants / Krishna Hanumanthu
85. Log symplectic pairs and mixed Hodge structures / Andrew Harder
86. Gaps between lc pairs and Klt pairs in a viewpoint of the minimal model theory / Kenta Hashizume
87. Constructing new Q-Fano threefolds using Laurent inversion / Liana Heuberger
88. Fano manifolds such that the tangent bundle is (not) big / Andreas Hoering
89. Geometric extension / Chris Hone and Geordie Williamson
90. An algebro-geometric higher Szemeredi lemma / Ehud Hrushovski
91. A dynamical approach to generalized Weil's Riemann hypothesis and semisimplicity / Fei Hu
92. Torelli problem on logarithmic sheaves / Sukmoon Huh
93. Minimal rational curves and 1-flat cone structures / Jun-Muk Hwang
94. A bound of the number of weighted blow-ups to compute the minimal log discrepancy for smooth 3-folds / Shihoko Ishii
95. The McKay correspondence / Yukari Ito
96. Shafarevich's conjecture for canonically polarized varieties revisited / Ariyan Javanpeykar, Steven Lu, Ruiran Sun and Kang Zuo
97. Symmetries of Fano varieties / Lena Ji
98. Minimal log discrepancies in dimension three / Chen Jiang
99. Equilateral convex triangulations of RP^2 with three conical points of equal defec / Nikita Kalinin
100. 1-dimensional K-moduli spaces of Fano 3-folds / Anne-Sophie Kaloghiros
101. A brief survey on stability of tangent bundles on Fano manifolds / Akihiro Kanemitsu
102. Are Klt Fano varieties of small volume stably rational? / Ilya Karzhemanov
103. New examples of surgery invariant counts in real algebraic geometry / Slava Kharlamov
104. Hodge sheaves for singular families / Sandor Kovacs
105. Secant varieties of real curves / Mario Kummer
106. Sextic double solids / Alexandra Kuznetsova
107. On effective cones of rational surfaces / Antonio Laface
108. The rational chow rings of M_7, M_8 and M_9 / Hannah Larson
109. A Neron-Ogg-Shafarevich criterion for K3 surfaces / Chris Lazda
110. Derived categories and motives of moduli spaces of vector bundles on curves / Kyoung-Seog Lee
111. Dominant rational maps from a very general hypersurface / Yongnam Lee
112. Valuative stability of polarised varieties / Eveline Legendre
113. Rational curves on Del Pezzo surfaces in positive characteristic / Brian Lehmann
114. Codimension 2 cycles of classifying spaces of low-dimensional algebraic tori / Nicole Lemire
115. Locally free twisted sheaves of infinite rank / Max Lieblich
116. Rational curves on K3 surfaces / Christian Liedtke
117. Automorphisms of projective hypersurfaces / Alvaro Liendo
118. Motivic invariants of birational maps Hsueh-Yung Lin / Evgeny Shinder
119. A motivic version of topological mirror symmetry / ransois Loeser
120. Poisson and symplectic geometry of the moduli spaces of Higgs bundles / Marina Logares
121. On non-rationality of degenerations of Del Pezzo surfaces / Konstantin Loginov
122. A conjecture on D algebras / Leonid Makar-Limanov
123. Fano threefolds of Picard rank 2 and volume 28 / Joseph Malbon
124. Birational involutions of the real projective plane fixing an irrational curve / Frederic Mangolte
125. Unirationality of instanton moduli space for small charges / Dimitri Markushevich and Alexander Tikhomirov
126. The defect of a cubic threefold / Lisa Marquand
127. The determinant of cohomology and moduli of lambda-connections / Johan Martens
128. Two remarks on asymptotically log Fano pairs / Jesus Martinez-Garcia
129. On K-stability of Calabi-Yau fibrations / Hattori Masafumi
130. On the (uni)rationality problem for hypersurfaces / Alex Massarenti
131. Transformations of transfinite diameter / Sione Ma`u
132. Perverse-Hodge octahedron / Mirko Mauri
133. A special rational surface / Massimiliano Mella
134. On the top-weight rational cohomology of A_g / Margarida Melo
135. Jordan property for automorphism groups / Sheng Meng
136. Geometry and arithmetic of equivariant compactifications of the affine space / Pedro Montero
137. Special variational Hodge conjecture for toric varieties / William Montoya
138. Tropical geometry and phylogenetic diversity / Han-Bom Moon
139. Fundamental groups of singularities of the MMP / Joaquin Moraga
140. A moduli space in the differential geometry world / David Mumford
141. Interview with David Mumford / Ivan Cheltsov and Jesus Martinez-Garcia
142. The Kawamata?Viehweg vanishing theorem for schemes / Takumi Murayama
143. Minimal exponent and Hodge filtrations / Mircea Mustata
144. Inversion of adjunction for quotient singularities / Yusuke Nakamura
145. On compatifying moduli and degenerations of K-trivial varieties / Yuji Odaka
146. K-stability and birational superrigidity for Fano 3-fold weighted hypersurfaces / Takuzo Okada
147. Moduli space of semiorthogonal decompositions /Shinnosuke Okawa
148. Stable irrationality of the very general quartic fiv / fold / John Christian Ottem /
149. Contact in algebraic and tropical geometry / Marco Pacini and Damiano Testa
150. Extended abstract of counting divisorial contractions with centre a cA_n-singularity / Erik Paemurru
151. Fine compactified Jacobians of nodal curves / Nicola Pagani
152. On polynomial automorphisms commuting with a simple derivation / Ivan Pan
153. K-moduli for log Fano complete intersections / Theodoros Stylianos Papazachariou
154. Cayley octads, plane quartic curves, Del Pezzo surfaces of degree 2, and double Veronese cones / Jihun Park
155. A Castelnuovo-Mumford regularity bound for threefolds with rational singularitie / Jinhyung Park
156. Moderately discontinuous algebraic topology and singularities / Maria Pe Pereira
157. Generic flexibility of cubic cones / Alexander Perepechko
158. Serre functors of semiorthogonal components / Alex Perry
159. Deformations of toric singularities and applications to K-moduli of Fano varieties / Andrea Petracci
160. Campana points on Fano varieties / Marta Pieropan
161. On canonical threefolds near the noether line / Roberto Pignatelli
162. K-stability and space sextic curves of genus three / Antoine Pinardin
163. On local-global principles and Galois cohomology / Alena Pirutka
164. Conic-line arrangements in the complex projective plane / Piotr Pokora
165. Hyperelliptic limits of quadrics through canonical curves and the super-Schottky locus / Alexander Polishchuk
166. General elephants for 3-fold extremal contractions / Yuri Prokhorov
167. Rationally connected rational double covers of primitive Fano varieties / Aleksandr Pukhlikov
168. Singularities and divisors in the moduli space of surfaces / Julie Rana
169. Sheaf counting of Hilbert schemes of points on C^4 / Jorgen Rennemo
170. Wall-crossing pathologies in three dimensions / Fatemeh Rezaee
171. K-polystability of smooth Fano SL_2-threefolds / Jack Rogers
172. Hodge-Riemann classes and schur polynomials / Julius Ross
173. The splendour of asymptotically log Del Pezzos / Yanir Rubinstein
174. Smoothing toroidal crossing Fano 3-folds / Helge Ruddat
175. An overview on mordell?Weil rank jumps for fibers of elliptic surfaces / Cecilia Salgado
176. Blow-ups with log canonical singularities / Gregory Sankaran
177. On birational boundedness of some Calabi?Yau hypersurfaces / Taro Sano
178. Equivariant solidity of the three-dimensional projective space / Arman Sarikyan
179. Near-rationality properties of norm varieties / Anand Sawant
180. Generalized hyperpolygons and applications / Laura Schaposnik
181. Equality in the Bogomolov-Miyaoka-Yau inequality in the non-general type case / Stefan Schreieder
182. Rational curves on Enriques surfaces, but only few / Matthias Schuett
183. Cohomology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture / Junliang Shen
184. Survey of the article on Atiyah class and sheaf counting on local Calabi-Yau fourfolds / Artan Sheshmani
185. Automorphism groups of complex elliptic surfaces / Constantin Shramov
186. Lebrun-Salamon conjecture from the effective nonvanishing for Fano manifolds / Robert Smiech
187. Partial order on involutive permutations and double Schubert cells / Evgeny Smirnov
188. Geometric aspects of Kahler-Einstein metrics on Klt pairs: a remark on optimal Bogomolov-Miyaoka-Yau inequality / Cristiano Spotti
189. Weak Del Pezzo surfaces with global vector fields / Claudia Stadlmayr
190. Local volumes of singularities and the mahler conjecture for convex bodies / Hendrik Suess
191. Higher order minimal families of rational curves on Fano manifolds / Taku Suzuki
192. An O-acyclic variety of even index / Fumiaki Suzuki
193. The Mukai model of M_7 / David Swinarski
194. Local effectivity in projective spaces /
195. Fermat type arrangements and the containment problem / Justyna Szpond
196. Birational properties of base spaces of smooth projective families of good minimal models / Behrouz Taji
197. Key varieties for prime Q-Fano threefolds of codimension 4 / Hiromichi Takagi
198. Deformations of F-pure and F-regular singularities / Shunsuke Takagi
199. On Mori fibre spaces in positive characteristic / Hiromu Tanaka
200. Rational curves on Fano threefolds / Sho Tanimoto
201. Delta invariants of quasi-smooth hypersurfaces / Luca Tasin
202. Real structures on almost homogeneous varieties / Ronan Terpereau
203. Mirror symmetry for fibrations and degenerations / Alan Thompson
204. On a logarithmic version of a theorem of Enriques / Sofia Tirabassi
205. Equivariant birational types / Yuri Tschinkel
206. Vector fields on canonically polarized surfaces / Nikos Tziolas
207. Noncommutative Del Pezzo surfaces / Kazushi Ueda
208. Exceptional collections on Σ_2 / Hokuto Uehara
209. Counts of secant planes to varieties, degenerations, and universal polynomials / Mara Ungureanu
210. Actions of Cremona groups on CAT(0) cube complexes / Christian Urech
211. Artin-Mumford counterexample, with generalizations, via Enriques surfaces / Alessandro Verra
212. Higher Fano manifolds / Nivedita Viswanathan
213. Global Brill-Noether theory over the Hurwitz space / Isabel Vogt
214. Positivity of the second exterior power of the tangent bundles / Kiwamu Watanabe
215. Pinched handle decompositions of finite simplicial complexes / Jean-Yves Welschinger
216. Concurrent exceptional curves on Del Pezzo surfaces of degree one and torsion points on elliptic fibrations / Rosa Winter
217. Rational maps via C^*-actions / Jaroslaw Wisniewski
218. On weighted Del Pezzo hypersurfaces / Joonyeong Won
219. Equivariant birational geometry of linear actions / Kaiqi Yang
220. Equivariant birational rigidity: around one question of Cheltsov and Kollar / Egor Yasinsky
221. Stringy motives and local fundamental groups of Klt surface singularities in arbitrary characteristic / Takehiko Yasuda
222. Degenerations, fibrations and mirror symmetry / Fenglong You
223. Stability of pencils of plane curves / Aline Zanardini
224. Jordan properties of automorphism groups of algebraic varieties and complex manifolds / Yuri Zarhin
225. Basis divisors and balanced metrics / Kewei Zhang
226. The moduli space of cubic surface pairs via the intermediate Jacobians of Eckardt cubic threefolds / Zheng Zhang
227. Equivariant geometry of singular cubic threefolds / Zhijia Zhang
228. Topological SYZ fibrations with discriminant in codimension 2 / Ilia Zharkov
229. Compact Kahler threefolds with the action of an abelian group of maximal dynamical rank / Guolei Zhong
230. Equivariant K-stability under finite group action / Ziwen Zhu
231. K-stability of Fano varieties via admissible flags / Ziquan Zhuang
232. Unbounded connected algebraic subgroups of birational transformations / Sokratis Zikas
233. Finite quotients of Cremona groups / Susanna Zimmermann
Copyright 2026
Hardback
ISBN 9781032710518
384 Pages
July 11, 2025 by Chapman & Hall
Exact Methods for Nonlinear PDEs is devoted to the description and practical application of effective analytical methods for finding exact solutions to nonlinear partial differential equations. It covers methods of generalized separation of variables, methods of functional separation of variables, the classical method of symmetry reductions, the direct method of symmetry reductions, the method of weak symmetry reductions, and the method of differential constraints. Furthermore, the book describes several simple methods for finding exact solutions to nonlinear PDEs that do not require specialized knowledge and minimize intermediate calculations. For the first time, the use of non-rigorous reasoning based on heuristic principles such as "from simple to complex" and "structural analogy of solutions" for deriving exact solutions to nonlinear PDEs is discussed. Each section includes numerous examples and exercises to help readers build practical skills in applying the methods. The presentation of the material is illustrated using equations of mass and heat transfer, hydrodynamics, wave theory, nonlinear optics, and other nonlinear equations of mathematical physics.
The key points that distinguish this book from others in the field include:
? Many methods are presented in a simpler and more visual format.
? The material is accessible to a broader range of readers than usual, including those with minimal training and no specialized mathematical education.
? Several simple methods for constructing exact solutions to nonlinear PDEs and delay PDEs, which minimize intermediate calculations are described.
? It emphasizes and details the practical use of non-rigorous reasoning to derive exact solutions for nonlinear PDEs.
The text is intended for a diverse audience including researchers, university professors, engineers, postgraduates, and students specializing in applied mathematics, theoretical physics, and engineering sciences.
1.Elementary Invariant Theory: Algebraic Equations and ODEs
2.First-Order Partial Differential Equations
3.Solution Methods for Functional Equations
4.Elementary Invariant Theory: Partial Differential Equations
5.Methods of Generalized Separation of Variables
6.Methods of Functional Separation of Variables
7.DirectMethod of Symmetry Reductions. Weak Symmetries
8.Classical Method of Symmetry Reductions
9.Differential Constraints Method
10.Transformations of Equations of Mathematical Physics
11.Using Simple Solutions to Construct Complex Solutions
12.Constructing Solutions of Complex Equations
Copyright 2025
Hardback
ISBN 9781032811529
416 Pages
May 26, 2025 by CRC Press
The theory of differential identities in associative rings and algebras is the basis of this monograph. Informally, an identical relation involving arbitrary elements in the underlying rings (or algebras) along with the unknown differential function is called a differential identity in a ring (or algebra). Invariant theory, non-commutative geometry, mathematical physics, and the theory of rings and algebras are just a few of the fields where this abstract theory has proved to be an effective instrument for solving a wide range of challenging issues, and as the twenty-first century has arrived, the theory of differential identities has found enormous applications in resolving a number of unresolved problems in the theory of rings.
This volume summarizes the findings and approaches that have significantly advanced the field during the previous three decades. The first chapter provides a brief introduction to the topic. The following three chapters cover the various kinds of derivations in rings and algebras as well as the interactions between the structure of some classes of rings with involution and the behavior of the underlying derivations, generalized derivations, skew derivations, and b-generalized derivations, as well as their corresponding properties. Chapter 5 explores the characterization of several kinds of higher derivable mappings and the structure of Lie and Jordan-type higher derivations. Although the book contains numerous applications
of the conclusions presented in these chapters, the last chapter mostly focuses on the application of derivations.
This research monograph is useful for researchers working in the area of differential identities in rings and algebras. It provides a comprehensive and authoritative account of research findings.
Preface. 1. Preliminaries. 2. Derivations in Rings and Algebras. 3. Derivations in Rings with Involution. 4. Generalized Derivations in Rings. 5. Higher Derivations in Rings and Algebras. 5. Applications of Derivations. References. Index. About the Monograph.