# Intellectual Life and the American South 1810 1860

Intellectual Life and the American South, 1810-1860: An Abridged Edition of Conjectures of Order Michael O'Brien has masterfully abridged his award-winning two-volume intellectual history of the Old South, Conjectures of Order.

Intellectual Life and the American South, 1810-1860: An Abridged Edition of Conjectures of Order

# Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures

Conjecture 5.66.1 Assume that α, A ∈ (0,∞). Show that every positive solution of Eq.(5.66.1) has a finite limit. In other words, the equilibrium ̄x of Eq.(5.66.1) is globally asymptotically stable. To the best of our knowledge, ...

Extending and generalizing the results of rational equations, Dynamics of Third Order Rational Difference Equations with Open Problems and Conjectures focuses on the boundedness nature of solutions, the global stability of equilibrium points, the periodic character of solutions, and the convergence to periodic solutions, including their periodic trichotomies. The book also provides numerous thought-provoking open problems and conjectures on the boundedness character, global stability, and periodic behavior of solutions of rational difference equations. After introducing several basic definitions and general results, the authors examine 135 special cases of rational difference equations that have only bounded solutions and the equations that have unbounded solutions in some range of their parameters. They then explore the seven known nonlinear periodic trichotomies of third order rational difference equations. The main part of the book presents the known results of each of the 225 special cases of third order rational difference equations. In addition, the appendices supply tables that feature important information on these cases as well as on the boundedness character of all fourth order rational difference equations. A Framework for Future Research The theory and techniques developed in this book to understand the dynamics of rational difference equations will be useful in analyzing the equations in any mathematical model that involves difference equations. Moreover, the stimulating conjectures will promote future investigations in this fascinating, yet surprisingly little known area of research.

# New Voyages to Carolina

See also Michael O'Brien, Conjectures of Order: Intellectual Life and the American South, 1810–1860, 2 vols. (Chapel Hill: University of North Carolina Press, 2004) 1:346–50. 7. William S. Powell, ed., Dictionary of North Carolina ...

New Voyages to Carolina offers a bold new approach for understanding and telling North Carolina's history. Recognizing the need for such a fresh approach and reflecting a generation of recent scholarship, eighteen distinguished authors have sculpted a broad, inclusive narrative of the state's evolution over more than four centuries. The volume provides new lenses and provocative possibilities for reimagining the state's past. Transcending traditional markers of wars and elections, the contributors map out a new chronology encompassing geological realities; the unappreciated presence of Indians, blacks, and women; religious and cultural influences; and abiding preferences for industrial development within the limits of "progressive" politics. While challenging traditional story lines, the authors frame a candid tale of the state's development. Contributors: Dorothea V. Ames, East Carolina University Karl E. Campbell, Appalachian State University James C. Cobb, University of Georgia Peter A. Coclanis, University of North Carolina at Chapel Hill Stephen Feeley, McDaniel College Jerry Gershenhorn, North Carolina Central University Glenda Elizabeth Gilmore, Yale University Patrick Huber, Missouri University of Science and Technology Charles F. Irons, Elon University David Moore, Warren Wilson College Michael Leroy Oberg, State University of New York, College at Geneseo Stanley R. Riggs, East Carolina University Richard D. Starnes, Western Carolina University Carole Watterson Troxler, Elon University Bradford J. Wood, Eastern Kentucky University Karin Zipf, East Carolina University

# Curriculum Accreditation and Coming of Age of Higher Education

On diaries and youth, see O'Brien, Conjectures of Order, 458. See also, Ruffin Wirt Tomlinson in Saunders, ed., “The Journal of Ruffin Wirt Tomlinson,” 90. North Carolina students' reasons for journalizing are consistent among other ...

This latest volume in Roger Geiger's distinguished series on the history of higher education begins with a rare glimpse into the minds of mid-nineteenth century collegians. Timothy J. Williams mines the diaries of students at the University of North Carolina to unearth a not unexpected preoccupation with sex, but also a complex psychological context for those feelings. Marc A. VanOverbeke continues the topic in an essay shedding new light on a fundamental change ushering in the university era: the transition from high schools to college.The secularization of the curriculum is a fundamental feature of the emergence of the modern university. Katherine V. Sedgwick explores a distinctive manifestation by questioning why the curriculum of Bryn Mawr College did not refl ect the religious intentions of its Quaker founder and trustees. Secularization is examined more broadly by W. Bruce Leslie, who shows how denominational faith ceded its ascendancy to "Pan-Protestantism."Where does the record of contemporary events end and the study of history begin? A new collection of documents from World War II to the present invites Roger Geiger's refl ection on this question, as well as consideration of the most signifi cant trends of the postwar era. Educators chafi ng under current attacks on higher education may take solace or dismay from the essay "Shaping a Century of Criticism" in which Katherine Reynolds Chaddock and James M. Wallace explore H. L. Mencken's writings, which address enduring issues and debates on the meaning and means of American higher education.

# The Antebellum Origins of the Modern Constitution

was kept aflame among the lowest white orders of society.90 Selectively quoting Burke to support the view that the presence of slavery gives liberty greater nobility, Tucker envisioned slavery as ... O'Brien, Conjectures of Order, 870.

This book argues that conflicts over slavery and abolition in the early American Republic generated a mode of constitutional interpretation that remains powerful today: the belief that the historical spirit of founding holds authority over the current moment. Simon J. Gilhooley traces how debates around the existence of slavery in the District of Columbia gave rise to the articulation of this constitutional interpretation, which constrained the radical potential of the constitutional text. To reconstruct the origins of this interpretation, Gilhooley draws on rich sources that include historical newspapers, pamphlets, and congressional debates. Examining free black activism in the North, Abolitionism in the 1830s, and the evolution of pro-slavery thought, this book shows how in navigating the existence of slavery in the District and the fundamental constitutional issue of the enslaved's personhood, Antebellum opponents of abolition came to promote an enduring but constraining constitutional imaginary.

# New Horizons in pro p Groups

order at most 227+ ?. Conjecture S. All sporadic 2 - groups of coclass r have order at most 22 +2 Conjecture P as stated in [ 24 ] has a misprint ; the period is stated there to be at most r – 1. We are grateful to the authors for ...

The impetus for current research in pro-p groups comes from four main directions: from new applications in number theory, which continue to be a source of deep and challenging problems; from the traditional problem of classifying finite p-groups; from questions arising in infinite group theory; and finally, from the younger subject of 'profinite group theory'. A correspondingly diverse range of mathematical techniques is being successfully applied, leading to new results and pointing to exciting new directions of research. In this work important theoretical developments are carefully presented by leading mathematicians in the field, bringing the reader to the cutting edge of current research. With a systematic emphasis on the construction and examination of many classes of examples, the book presents a clear picture of the rich universe of pro-p groups, in its unity and diversity. Thirty open problems are discussed in the appendix. For graduate students and researchers in group theory, number theory, and algebra, this work will be an indispensable reference text and a rich source of promising avenues for further exploration.

# Mathematical Argumentation in Middle School The What Why and How

Figure 4.1 Teacher Writes Out and Organizes Students' Conjectures With this order, she would address her instructional goal for students to apply and extend their use of numeric representations to developing algebraic representations to ...

Get them talking: Your formula for bringing math concepts to life! Want your middle schoolers to intelligently engage with mathematical ideas? Look no further. This research-based gem brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive—all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding. Immediately engage students in fun, classroom-ready argumentation activities Help students explore—and take ownership of—mathematical ideas and concepts Promote precise use of mathematical language Includes games, vignettes, a rich companion website, sample tasks, and links to online tools. Bring well-planned, well-constructed mathematical discourse to life in your classroom today!

# Summa Theologica Volume 3 Part II Second Section

Again under the head of prudence he mentions conjecture, shrewdness, sense and understanding. And another Greek philosopher* says that ... The third method is to employ conjectures in order to Q. 48 Arr. Pt. u-n 1394 VIRTUES AND VICES 394.

"The Summa Theologica is the best-known work of Italian philosopher, scholar, and Dominican friar SAINT THOMAS AQUINAS (1225 1274), widely considered the Catholic Church s greatest theologian. Famously consulted (immediately after the Bible) on religious questions at the Council of Trent, Aquinas s masterpiece has been considered a summary of official Church philosophy ever since. Aquinas considers approximately 10,000 questions on Church doctrine covering the roles and nature of God, man, and Jesus, then lays out objections to Church teachings and systematically confronts each, using Biblical verses, theologians, and philosophers to bolster his arguments. In Volume III, Aquinas addresses: faith and heresy charity peace and war mercy, anger, and justice prayer truth and much more. This massive work of scholarship, spanning five volumes, addresses just about every possible query or argument that any believer or atheist could have, and remains essential, more than seven hundred years after it was written, for clergy, religious historians, and serious students of Catholic thought."

# Introductory Map Theory

Because triangulations of order n have exactly 3n − 6 edges and 2n − 4 faces, all the small face embeddings are not yet on the sphere for n ≥ 4. R2.4 Conjecture. Any graph of order at least six without cutedge has a small face proper ...

As an introductory work, this book contains the elementary materials in map theory, includingembeddings of a graph, abstract maps, duality, orientable and non-orientable maps, isomorphisms of maps and the enumeration of rooted or unrooted maps, particularly, thejoint tree representation of an embedding of a graph on two dimensional manifolds, whichenables one to make the complication much simpler on map enumeration. All of theseare valuable for researchers and students in combinatorics, graphs and low dimensionaltopology.A Smarandache system (Sigma;R) is such a mathematical system with at leastone Smarandachely denied rule r in R such that it behaves in at least two different wayswithin the same set Sigma, i.e., validated and invalided, or only invalided but in multiple distinctways. A map is a 2-cell decomposition of surface, which can be seen as a connectedgraphs in development from partition to permutation, also a basis for constructing Smarandachesystems, particularly, Smarandache 2-manifolds for Smarandache geometries.

# Automated Deduction CADE 19

It also highlights the set of integers each conjecture applies to, so the user can make more informed value judgements. ... At present – to keep the system simple to use – the user cannot prune/order conjectures using the plethora of ...

The refereed proceedings of the 19th International Conference on Automated Deduction, CADE 2003, held in Miami Beach, FL, USA in July 2003. The 29 revised full papers and 7 system description papers presented together with an invited paper and 3 abstracts of invited talks were carefully reviewed and selected from 83 submissions. All current aspects of automated deduction are discussed, ranging from theoretical and methodological issues to the presentation of new theorem provers and systems.

# American journal of mathematics

As for these forms , they gave two more conjectures similar to the first . But , actually the conjecture about F2 needs a modification . ... The generators are ( 1 + √2 ) ( of order 4 ) and 3 ( of order 2 ) modulo 40√√ .

# Point Counting and the Zilber Pink Conjecture

tuk > Mi = = idea is to expand the entries in Taylor series with the remainder in order to register cancellation of low - order terms . Then the remaining terms have high orders and are small . But one also does not want to have too ...

Point-counting results for sets in real Euclidean space have found remarkable applications to diophantine geometry, enabling significant progress on the André–Oort and Zilber–Pink conjectures. The results combine ideas close to transcendence theory with the strong tameness properties of sets that are definable in an o-minimal structure, and thus the material treated connects ideas in model theory, transcendence theory, and arithmetic. This book describes the counting results and their applications along with their model-theoretic and transcendence connections. Core results are presented in detail to demonstrate the flexibility of the method, while wider developments are described in order to illustrate the breadth of the diophantine conjectures and to highlight key arithmetical ingredients. The underlying ideas are elementary and most of the book can be read with only a basic familiarity with number theory and complex algebraic geometry. It serves as an introduction for postgraduate students and researchers to the main ideas, results, problems, and themes of current research in this area.

# Automated Deduction CADE 25

For CASC-25 the divisions were: – THF: Typed Higher-order Form theorems (axioms with a provable conjecture). – THN: Typed Higher-order form Non-theorems (axioms with a countersatisfiable conjecture, and satisfiable axiom sets).

This book constitutes the proceedings of the 25th International Conference on Automated Deduction, CADE-25, held in Berlin, Germany, in August 2015. The 36 revised full papers presented ( 24 full papers and 12 system descriptions) were carefully reviewed and selected from 85 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations and practical experience.

# Handbook of Graph Theory

CONJECTURES The 1 - Factorization Conjecture : Let G be a simple graph of even order n . If G is regular with A ( G ) ≥ n / 2 , then x ' ( G ) = A ( G ) ; that is , G has a 1 - factorization . ( See [ Wa97 ; Ch . 19 ] . ) ...

The Handbook of Graph Theory is the most comprehensive single-source guide to graph theory ever published. Best-selling authors Jonathan Gross and Jay Yellen assembled an outstanding team of experts to contribute overviews of more than 50 of the most significant topics in graph theory-including those related to algorithmic and optimization approach

# Revue Roumaine de Math matiques Pures Et Appliqu es

This chapter ends with the statement of the Well conjectures . In order to motivate the cohomological attacks on the Weil conjectures , the author describes in Chapter 10 how one can prove the analogous conjectures ( except the Riemann ...

# Codes From Difference Sets

Conjecture 4.4. For any f e GF(2")[x], we define Df = {f(x(x + ... The reader is invited to work on these conjectures. ... It was verified by Gordon that the Prime Power Conjecture (PPC) is true for order 6 s 2,000,000 [Gordon (1994)].

This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.

# Multi Agent Systems and Applications IV

Contrary to classical approaches, our contribution relies on agents' dialectical reasoning: in order to take into account the ... allowing agents to progressively prune objections, solve conjectures and elaborate solutions step by step.

The aim of the CEEMAS conference series is to provide a biennial forum for the presentation of multi-agent research and development results. With its p- ticular geographicalorientation towards Central and Eastern Europe, CEEMAS has become an internationally recognised event with participants from all over the world. After the successful CEEMAS conferences in St. Petersburg (1999), Cracow (2001) and Prague (2003), the 2005 CEEMAS conference takes place in Budapest. The programme committee of the conference series consists of est- lished researchers from the region and renowned international colleagues, sh- ing the prominent rank of CEEMAS among the leading events in multi-agent systems. In the very competitive ?eld of agent oriented conferences and workshops nowadays(suchasAAMAS,WI/IAT,EUMAS,CIA,MATES)thespecialpro?le of CEEMAS is that it is trying to bridge the gap between applied research achievements and theoretical research activities. Our ambition is to provide a forum for presenting theoretical research with an evident application potential, implemented application prototypes and their properties, as well as industrial case studies of successful (but also unsuccessful) agent technology deployments. This is why the CEEMAS proceedings volume provides a collection of research and application papers. The technical research paper section of the proceedings (see pages 11–499) contains pure research papers as well as research results in application settings while the application papers section (see pages 500–530) contains papers focused on application aspects. The goal is to demonstrate the real life value and commercial reality of multi-agent systems as well as to foster communication between academia and industry in this ?eld.

# Conjecture and Proof

We shall say that a is approximable by rationals to order s if there is a constant c ( depending only on a and s ) such that р с a ( 1 ) a q \$ for infinitely many rational numbers p / q . The last theorem of the previous section states ...

The Budapest semesters in mathematics were initiated with the aim of offering undergraduate courses that convey the tradition of Hungarian mathematics to English-speaking students. This book is an elaborate version of the course on Conjecture and Proof. It gives miniature introductions to various areas of mathematics by presenting some interesting and important, but easily accessible results and methods. The text contains complete proofs of deep results such as the transcendence of \$e\$, the Banach-Tarski paradox and the existence of Borel sets of arbitrary (finite) class. One of the purposes is to demonstrate how far one can get from the first principles in just a couple of steps. Prerequisites are kept to a minimum, and any introductory calculus course provides the necessary background for understanding the book. Exercises are included for the benefit of students. However, this book should prove fascinating for any mathematically literate reader.

# The Poincar Conjecture

By 1909, Einstein would be recognized as a major thinker, on the order of a Poincaré. The relationship between the two men was complex: They met only once, at a conference in 1911 in Solvay, Belgium. Poincaré had a very high opinion of ...

The Poincaré Conjecture tells the story behind one of the world’s most confounding mathematical theories. Formulated in 1904 by Henri Poincaré, his Conjecture promised to describe the very shape of the universe, but remained unproved until a huge prize was offered for its solution in 2000. Six years later, an eccentric Russian mathematician had the answer. Here, Donal O’Shea explains the maths behind the Conjecture and its proof, and illuminates the curious personalities surrounding this perplexing conundrum, along the way taking in a grand sweep of scientific history from the ancient Greeks to Christopher Columbus. This is an enthralling tale of human endeavour, intellectual brilliance and the thrill of discovery.

# Polynomial Automorphisms

In fact the original conjecture, due to Dixmier, was formulated for n = 1 in [89], 1968. ... to a weak version of the Dixmier Conjecture. Therefore we consider on An the so-called order filtration (Appendix E) F(0) C F(1) C F(2) C . .

Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest. This book, the first in the field, collects many of the results scattered throughout the literature. It introduces the reader to a fascinating subject and brings him to the forefront of research in this area. Some of the topics treated are invertibility criteria, face polynomials, the tame generators problem, the cancellation problem, exotic spaces, DNA for polynomial automorphisms, the Abhyankar-Moh theorem, stabilization methods, dynamical systems, the Markus-Yamabe conjecture, group actions, Hilbert's 14th problem, various linearization problems and the Jacobian conjecture. The work is essentially self-contained and aimed at the level of beginning graduate students. Exercises are included at the end of each section. At the end of the book there are appendices to cover used material from algebra, algebraic geometry, D-modules and Gröbner basis theory. A long list of ''strong'' examples and an extensive bibliography conclude the book.