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SAT / ACT Prep Online Guides and Tips. The average is **Christmas Carol**, definitely lower than a perfect 5! Taking an the gate theory of pain suggests that AP class this year? You might be wondering about average AP scores, or what good AP scores are for certain classes. Or if you are thinking about taking AP exams in **Scrooge in A** the future, you might want to know which exams have the highest passing rates.
In this post, we will break down the average score for each AP test, as well as the average passing rate. We will also show you how to interpret this info and how to *study*, use it to *Scrooge in A Carol Essay*, make decisions about your schedule. Instead of giving you an overall average score for all AP tests, we will show you the average score for every AP exam.

We break it down by test because every AP test is different. Its important to know the average score for whichever test you are taking or thinking about taking. We will also explore how you can use this infoand learn why the exams with the highest passing rates are not the easiest! But first, the data. The table contains the **study**, national average scores for each AP exam from 2017.

Remember that AP exams are scored from 1 to 5, with 3 and higher considered passing rates. We have sorted the exams from **Scrooge in A Christmas** highest average score to lowest.
Take a look: Via College Board. *Effect*? Check out the link for a complete distribution of scores for each AP exam. *Scrooge In A Christmas*? One very important fact to note is that high average scores don't correspond to the easiest exams! Chinese, Calculus BC, Physics C Mechanics, Japanese, and *the immoralist* Spanish Language are the AP tests with the highest average scores, but they are all known to be quite difficult. Also note that native speakers, or students with experience living abroad, tend to take the AP language exams, which inflates their average scores (for the average of those who learned in a classroom, check the Standard score).
Furthermore, some of the tests with the **in A Christmas Carol**, lowest averages are often regarded as some the **the immoralist**, easiest APsHuman Geography, Environmental Science, and US Government. So why are their passing rates so low?

This is because freshmen and sophomores might take these as their first-ever AP classes. Even though the content is easier than, say, Calculus, all AP exams are tough and could be hard for a younger student to do well on. Its also possible that students simply dont study enough for the easier exams because they underestimate them. To sum up, the average score can say more about the **Scrooge in A Carol**, students taking the exam than the exam itself. Dont sign up for BC Calculus just because the **the gate that**, average score is super high.

And by the same token, dont avoid AP Environmental Science because the average score is **Scrooge Christmas**, relatively low.
Focus on your own strengths and interests when signing up for AP classes! Beyond the **the great legacy**, basic averages, its helpful to have some context about **Christmas Carol Essay**, what a good AP score is. A score of 3 or higher is generally considered good, because that means you passed the exam! A 4 is considered very good, and a 5 is especially impressive since it is the highest score.

Also keep in mind that every college sets its own policy about AP credit. Some schools only give credit for scores of **harry study** 4 or 5. *In A Essay*? Check the AP credit database to find out the AP credit policy for schools you're interested in. But with that in mind, lets look at which AP exams have the highest passing ratesa.k.a. rates of scores over *the immoralist* 3. We also note the percentage of students who get a 5, the highest score. Source: College Board. The Standard language scores represent the students taking language AP exams who only *Christmas* took the language in school. *The Butterfly Effect Movie Review*? This is why the Standard passing rates are lower than the Total passing rate for the language (that rate includes native speakers and students with experience living abroad).
Again, note that some of the toughest examslike Chinese and BC Calculushave very high passing rates. Notice also the exams with very low 5 rates (below 10%) , including English Language, English Literature, and Biology. *Scrooge In A Carol Essay*? It will look especially impressive if you can earn a 5 on these tests!

So Which AP Classes Should You Take? Obviously the goal of **alexander** taking an AP class is to pass the exam. On a practical level, you dont want to pay the $94 exam fee and *in A Christmas Carol Essay* have it go to waste by failing the **on The Author**, test. *Scrooge In A Carol*? However, be careful about signing up for exams based on their average scores alone. As we saw above, some of the toughest exams have the highest passing rates, and some of the easiest exams have the lowest ones.
Make sure to do your research before signing up for an AP class and make sure its the right fit for you!

Finally, note that these are the national averages. The passing rates for **Undoing Trauma in Public**, different subjects could be very different at **in A Christmas** your school. If you want to find out the passing rates for these classes at **on The Being** your school, talk to your guidance counselor and they can help you find that info. For example, some teachers have passing rates for their AP classes above 90%.
If you have a teacher like that at your school, and they teach an in A Christmas Carol AP subject you are interested in, you will likely have a very high chance of passing. One last word of **the great legacy** advice: check out our scoring guide to see how AP scores are calculated to help you develop a target raw score to help you pass.

Understanding how the **Scrooge Christmas**, exam is scored is a very important step in preparing for AP tests. *Harlow Study*? Get tips on the SAT from our 1600 Full Scorer you can also put the same techniques to use when studying for AP exams, especially the **in A Christmas**, multiple choice sections! Want to improve your SAT score by **harry** 160 points or your ACT score by 4 points? We've written a guide for each test about the top 5 strategies you must be using to have a shot at improving your score. Download it for free now: Have friends who also need help with test prep?
Share this article! Halle Edwards graduated from Stanford University with honors. In high school, she earned 99th percentile ACT scores as well as 99th percentile scores on SAT subject tests. She also took nine AP classes, earning a perfect score of 5 on seven AP tests. *In A Christmas Essay*? As a graduate of a large public high school who tackled the college admission process largely on her own, she is passionate about **harlow**, helping high school students from different backgrounds get the knowledge they need to *in A*, be successful in the college admissions process. *Essay Argument*? You should definitely follow us on social media.

You'll get updates on our latest articles right on your feed. Follow us on all 3 of our social networks: Have any questions about this article or other topics?
Ask below and *Scrooge in A Christmas* we'll reply! Series: How to Get 800 on Each SAT Section: Series: How to Get to 600 on Each SAT Section: Series: How to Get 36 on Each ACT Section: Our hand-selected experts help you in **harry harlow study** a variety of other topics! Looking for Graduate School Test Prep? Check out our top-rated graduate blogs here: Get the latest articles and test prep tips!

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Scrooge in A Christmas Carol by Charles Dickens

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Ph.D. Recipients and their Thesis Abstracts.
Quasisymmetric Functions and Flag Enumeration in Eulerian Posets.
Abstract: We study the algebraic and enumerative combinatorial aspects of Eulerian posets and their quasisymmetric generating functions. These generating functions span the so-called peak algebra Pi, which originated with Stembridge's theory of enriched P -partitions. Remarkably, many constructs in the peak algebra that are natural in the context of enriched P -partitions are also important from the viewpoint of flag enumeration. For example, we show that the *Christmas Carol Essay* fundamental basis of peak functions arising from enriched P -partitions of chains is precisely the basis that is needed to properly encode the *on The Argument for Shakespeare Being the Real Author* cd -index, a common invariant in the study of convex polytopes and **Scrooge Christmas** Eulerian posets. As another example, the descents-to-peaks map, which relates the ordinary and enriched theories of P -partitions, turns out to be important for computing the flag-enumerative information of an oriented matroid based on that of the *on The for Shakespeare Author* underlying matroid.

We introduce a family of **Scrooge in A Christmas Essay**, Eulerian posets, called posets of signed order ideals. Each of these posets is defined by appropriately signing a distributive lattice. **Alexander Legacy**? We establish that the flag-enumerative relationship between a poset of signed order ideals and its underlying distributive lattice is completely analogous to that between an oriented matroid and its underlying matroid. Furthermore, we show that these posets are EL-shellable, they have non-negative cd -indices, and their quasisymmetric generating functions enumerate the enriched P -partitions of certain labeled posets.
We analyze the (external) Hopf algebra structure on Pi, showing it to be dual to the concatenation Hopf algebra on letters of odd degree. **Christmas Essay**? Consequently, Pi is *alexander legacy*, freely generated as a commutative algebra. Upon closer inspection of the generators, we find that Pi is *Scrooge in A Carol*, free as a module over the ring of Schur Q -functions. Much of our analysis builds on basic properties of a monomial-like basis for the peak algebra, as well as a recursively defined basis of eigenvectors for the descents-to-peaks map. We give a simple criterion, in **Health Practice**, terms of this monomial basis, for determining when an element of Pi is symmetric.

Homological Results in Commutative Algebra. Abstract: We discuss a bound on the multiplicity of ideals in the first chapter. Herzog and Srinivasan have conjectured that for any homogeneous k -algebra of codimension d , the multiplicity is bounded by. where $M_i$ is the maximal degree of an i th syzygy. Using the minimal free resolutions as constructed by Peeva and Sturmfels, we show that this bound holds for codimension 2 lattice ideals. The topic of chapter two is ideals having three generators. It is known due to work by Burch and by Kohn that any projective dimension may be realized by a 3-generated ideal. Buchsbaum and Eisenbud conjectured that the tail of any resolution may be realized by a 3-generated ideal.

This result and a generalization was shown by Bruns. We introduce a family of ideals and prove that for each n the resolution of the ideal in n variables from the family has the same tail as the Koszul resolution on those n variables.
In chapter three we attempt to extend the *in A Christmas Carol* result of **the immoralist**, chapter two to **Christmas Carol Essay**, ideals generated by **legacy** binomials. We display binomial examples in 4, 5 and 6 variables. A binomial example having the same tail as the Koszul complex for n = 7 is not found, but we do display 3-generated binomial examples having projective dimensions seven and eight.
Shuffles and Shellings via Projection Maps.
Abstract: Projection maps which appear in the theory of buildings and oriented matroids are closely related to the notion of **Scrooge in A Carol**, shellability. This was first observed by **alexander legacy** Bjorner. In the first chapter, we give an axiomatic treatment of either concept and show their equivalence. We also axiomatize duality in this setting. As applications of **in A Essay**, these ideas, we prove a duality theorem on buildings and give a geometric interpretation of the flag h vector.

The former may be regarded as a q -analogue of the Dehn-Sommerville equations. We also briefly discuss the connection with the random walks introduced by Bidigare, Hanlon and Rockmore.
The random-to-top and the riffle shuffle are two well-studied methods for shuffling a deck of cards. These correspond to the symmetric group S_n , i.e., the Coxeter group of type A_ . In the second chapter, we give analogous shuffles for the Coxeter groups of **movie review**, type B_n and D_n . These can be interpreted as shuffles on a signed'' deck of **Christmas Essay**, cards. With these examples as motivation, we abstract the notion of **Undoing Historical Health Practice Essay**, a shuffle algebra which captures the connection between the algebraic structure of the shuffles and the geometry of the Coxeter groups. We also give new joker shuffles of type A_ and briefly discuss the generalization to **Christmas**, buildings which leads to q -analogues.
Subspace Subcodes and **Undoing Historical Trauma in Public Essay** Generalized Coset Codes.
Abstract: This dissertation considers codes that are formed using certain subsets of **Scrooge Essay**, algebraic error-control codes and signal space codes. **Study**? We first consider subspace subcodes of **in A Carol**, Reed-Solomon (SSRS) codes. We prove a conjecture of Hattori concerning how to identify subspaces that give an SSRS code whose dimension exceeds a certain lower bound.

We next consider generalized coset codes, which are built using partitions of signal space codes. We extend the concepts of generalized coset codes in Euclidean space by **harry harlow** defining generalized coset codes in Lee space. We prove that all linear codes over Z _ m are realizable as these new Lee-generalized coset codes. This implies that linear codes over Z _ m have desirable symmetry properties. We also discuss some relationships among integer lattices, linear codes over Z _4, and generalized coset codes.
Enumeration in Geometric Lattices and **Essay** the.

Abstract: This work primarily deals with questions relating to the enumeration of chains in geometric lattices. The study of geometric lattices arose in **the great**, the process of characterizing the lattices of subspaces formed by **Scrooge Christmas Carol Essay** a finite set of points in projective or affine space, and ordered by inclusion. More generally geometric lattices encode the structure of matroids (or combinatorial geometries), which take an axiomatic approach to the concept of **the immoralist**, dependence.
The flag Whitney numbers of a geometric lattice count the *Scrooge Carol* number of chains of the lattice with elements having specified ranks. We are interested in the linear inequalities satisfied by the flag Whitney numbers.
We present a lower bond on the flag Whitney numbers of a lattice in terms of **Historical**, its rank and number of atoms. **In A Carol Essay**? We also show that all flag Whitney numbers are simultaneously minimized by the lattice corresponding to the near pencil arrangement of points in R ^ n . Next we focus on rank 3 geometric lattices and give a collection of **the great**, inequalities which imply all the *Scrooge Christmas Carol Essay* linear inequalities satisfied by the flag Whitney numbers of **Essay on The for Shakespeare Being**, rank 3 geometric lattices. **Scrooge In A**? We further describe the *effect movie review* smallest closed convex set containing the flag Whitney numbers of rank 3 lattices corresponding to oriented matroids.
The ab -index is a polynomial associated to a lattice which contains all of the *Scrooge Carol* information regarding the flag Whitney numbers. We give a recurrence relation for the ab -index of **Health**, families of lattices satisfying a particular set of conditions.

We also give a collection of inequalities for the ab -index of geometric lattices.
Finally, we turn our attention to the group algebra of the symmetric group. The peak set of a permutation $sigma$ is the set $ $. We prove the existence of a subalgebra of Solomon's descent algebra in which elements are sums of permutations that share a common peak set.
Linear Inequalities for Flag f-Vectors of Polytopes.
Abstract: Here we study the combinatorics of polytopes. A polytope P is the convex hull of a finite set of points in R ^ d , and its boundary is a collection of lower-dimensional polytopes known as the faces of **Scrooge in A Christmas**, P . The flag f -vector of **alexander the great legacy**, P counts the *Scrooge in A Carol Essay* faces of each dimension and their incidences with one another. **Argument For Shakespeare Being**? We would like to know what linear inequalities the entries of the *Carol* flag f -vector satisfy.
First we present some of the history of this problem, along with the necessary mathematical background. We discuss several special classes of polytopes, including simplicials, simples, cubicals and **alexander the great legacy** zonotopes, whose flag f -vectors satisfy inequalities not satisfied by all polytopes.

Then we define Stanley's toric g -vector, which can be used to generate many linear inequalities for flag f -vectors. We prove Meisinger's conjecture that some of these inequalities are implied by others. **In A Christmas Essay**? In addition, we consider the cd -index, another source of **alexander the great**, many inequalities. We show that not all of these are consequences of the non-negativity of the *Scrooge Christmas Carol Essay* toric g -vector.
We then use linear inequalities satisfied by lower-dimensional polytopes to generate linear relations satisfied by simplicial, simple, k -simplicial and k -simple polytopes, and cubical zonotopes. We also examine a g -vector for cubical polytopes proposed by Adin and give evidence that supports the conjecture g _2 = 0. **Suggests That**? In particular, we show this to hold for **Scrooge in A Carol Essay** the class of almost simple cubical polytopes, where one might expect it is most likely to fail.

Next we improve upon previously known linear inequalities satisfied by zonotopes. Finally, we construct examples of another special class of polytopes, the self-dual polytopes.
Derived Categories of Twisted Sheaves on Calabi-Yau Manifolds.
Abstract: This dissertation is primarily concerned with the study of **Undoing Trauma in Public**, derived categories of twisted sheaves on **Scrooge Christmas Essay**, Calabi-Yau manifolds. **Effect Movie**? Twisted sheaves occur naturally in **Scrooge Christmas Carol Essay**, a variety of **control of pain suggests that**, problems, but the most important situation where they are relevant is in **in A Christmas Carol**, the study of moduli problems of **control of pain suggests**, semistable sheaves on **Scrooge Christmas Carol Essay**, varieties. Although universal sheaves may not exist as such, in many cases one can construct them as twisted universal sheaves. In fact, the twisting is an **Undoing Trauma Practice**, intrinsic property of the moduli problem under consideration.
A fundamental construction due to Mukai associates to a universal sheaf is a transform between the derived category of the original space and the derived category of the moduli space, which often turns out to be an equivalence. In the present work we study what happens when the universal sheaf is replaced by a twisted one.

Under these circumstances we obtain a transform between the derived category of sheaves on the original space and the derived category of twisted sheaves on the moduli space.
The dissertation is *Christmas Essay*, divided into two parts. The first part presents the *control theory suggests that* main technical tools: the Brauer group, twisted sheaves and their derived category, as well as a criterion for checking whether an integral transform is an equivalence (a so-called Fourier-Mukai transform). **Scrooge In A Christmas Carol**? When this is the case we also obtain results regarding the cohomological transforms associated to the ones on the level of derived categories.
In the second part we apply the theoretical results of the *Undoing Historical in Public* first part to a large set of relevant examples. We study smooth elliptic fibrations and the relationship between the theory of twisted sheaves and Ogg-Shafarevich theory, K _3 surfaces, and elliptic Calabi-Yau threefolds. In particular, the study of elliptic Calabi-Yau threefolds leads us to an example which is likely to **in A Essay**, provide a counterexample to **Essay on The**, the generalization of the Torelli theorem from K _3 surfaces to threefolds. A similarity between the examples we study and certain examples considered by Vafa-Witten and Aspinwall-Morrison shows up, although we can only *Scrooge Christmas* guess the relationship between these two situations at the moment.
Representations and Characters of an Extension of SL(3,R) by an Outer Automorphism.

Abstract: Not available.
Centralizers of Finite Subgroups of Automorphisms and Outer Automorphisms of Free Groups.
Abstract: In this work we consider centralizers of finite subgroups of automorphisms and outer automorphisms of a finitely generated free group. The work of S. Krstic reveals that the centralizer of a finite subgroup of outer automorphisms (resp. automorphisms) of a free group is generated by isomorphisms and **in Public Practice** Nielsen transformations of reduced G -graphs (resp. pointed G -graphs). Here this characterization is exploited to **in A Christmas Essay**, find necessary and sufficient conditions for the centralizer of a finite subgroup of outer automorphisms (resp. automorphisms) to be finite.
Cohomology of Aut(F_n)
Abstract: For odd primes p , we examine the Farrell cohomology H ^*(Aut( F _ p 1)); Z _ p )) of the group of automorphisms of a free group F _ p 1) on 2( p 1) generators, with coefficients in the integers localized at the prime ( p )subset Z . This extends results in [12] by Glover and Mislin, whose calculations yield H ^*(Aut( F_n ); Z _ p )) for n in p 1, p and is concurrent with work by Chen in [9] where he calculates H ^*(Aut( F_n ); Z _ p )) for n in p +1, p +2. The main tools used are Ken Brown's Normalizer spectral sequence from [7], a modification of **the great**, Krstic and **Scrooge Carol Essay** Vogtmann's proof of the contractibility of fixed point sets for outer space in [19], and a modification of the Degree Theorem of Hatcher and Vogtmann in [15].
Other cohomological calculations in the paper yield that H ^5( Q_m ; Z ) never stabilizes as m toinfty, where Q_m is the *the gate theory of pain suggests that* quotient of the spine X_m of auter space introduced in [15] by Hatcher and Vogtmann. This contrasts with the theorems in [15] where various stability results are shown for H^n (Aut( F_m ); Z ), H^n (Aut( F_m ); Q ), and H^n ( Q_m ; Q ).

Actions of Artin Groups and Automorphism Groups on R -Trees.
Abstract: This dissertation determines the *Carol* ways in which two classes of groups act by isometries on R -trees. The first groups studied are the two-generator Artin groups A _ n +1, where 2 n +1 is half the length of the relator. In the case where 2 n +1 is prime, all abelian and non-abelian A _ n +1-actions are found, thus determining by Bass-Serre theory all of the graph of groups decompositions of A _ n +1. The same techniques are applied to a three-generator Artin group, the braid group on **Argument for Shakespeare Author**, four strands, enabling a description of all of its actions on R -trees. The second groups studied are the pure symmetric automorphism groups P Sigma_ n of a free group on **in A Carol Essay**, n generators; these groups consist of the automorphisms mapping every generator to a conjugate of itself.

All exceptional abelian P Sigma_ n -actions on R -trees are found in the sense that their length functions are given. This information determines the Bieri-Neumann-Strebel invariant of P Sigma_ n using Brown's characterization. The invariant tells which normal subgroups of P Sigma_ n with abelian quotient are finitely generated.
Internal Categories and Quantum Groups.
Abstract: Let be a monoidal category with equalizes that are preserved by the tensor product. The notion of categories internal to , and extending the usual notion of internal categories, which is obtained when is a category with products and equalizers.
The basic theory of **harlow study**, internal categories is developed and several applications to quantum groups are found. Delta categories are defined; these are algebraic objects that generalize groups or bialgebras, in the sense that attached to **Scrooge Christmas Carol**, them there is a monoidal category of representations. Quantum groups are constructed from **control**, delta categories.

In particular a construction of quantum groups generalizing that of Drinfeld and Jimbo is presented. An invariant of **Scrooge Christmas**, finite dimensional quasitriangular Hopf algebras is constructed.
Homological Methods in the Theory of Splines.
Abstract: This thesis is devoted to **on The for Shakespeare the Real Author**, the study of splines, which are piecewise polynomial functions of a prescribed order of smoothness on **Scrooge**, a triangulated (or otherwise polyhedrally subdivided) region Delta of R ^ d. The set of splines of **harry harlow study**, degree at most k (i.e. each individual polynomial is of degree at most k ) forms a vector space C^r_k (Delta).
It turns out that a good way to study C^r_k (Delta) is to **Scrooge in A Christmas Carol**, embed Delta in R ^ d +1, and form the cone hatDelta of Delta with the *Essay for Shakespeare the Real Author* origin. Then the set of splines (of all degrees) on hatDelta is *Scrooge in A Christmas*, a graded module C^r (hatDelta) over the polynomial ring R in **control theory of pain suggests that**, d +1 variables, and the dimension of **Scrooge Carol**, C^r_k (Delta) is the dimension of C^r (hatDelta) in degree exactly k.
The thesis follows the work of **the great**, Billera and Rose, who defined a chain complex such that C^r_k (Delta) appears as the top homology module, and **Scrooge Christmas Carol Essay** approaches the problem from the viewpoint of homological algebra (but using a different chain complex (Cal R/Cal J)).
First, we analyze the lower homology modules in the planar case, and prove that the module C^r (hatDelta) is free if and **the butterfly effect** only if the module H_ 1(Cal R/Cal J) vanishes. We prove that this latter module has finite length, and is nonzero whenever Delta has positive genus. For a fixed configuration Delta, we prove a criterion which gives sufficient conditions for C^r (hatDelta) to be nonfree, i.e. for H_ 1(Cal R/Cal J) to be nonzero.
Next, we relate the local geometry of Delta (the arrangement of lines at each vertex) to ideals generated by powers of homogeneous linear forms in R [ x , y ], and completely describe the resolutions possible for such ideals.

This result, together with results on the homology modules, allows us to determine the Hilbert polynomial for C^r (hatDelta).
In the final chapter, we consider the situation for an arbitrary d -dimensional simplicial complex Delta. Generalizing the *Christmas Essay* planar results, we obtain bounds on the dimension of the homology modules H_i (Cal R/Cal J) for **control of pain suggests** all i d . Specializing to the case where Delta is *Essay*, a topological d -ball, we use a spectral sequence argument to relate the *effect movie* lower homology modules to C^r (hatDelta). For example, we prove that C^r (hatDelta) is free iff H_i (Cal R/Cal J) is zero for all i d . **Scrooge In A Carol Essay**? As a corollary, we find if C^r (hatDelta) is *the butterfly movie review*, free, then C^r (hatDelta) is determined entirely by local data.
Solving Sparse Polynomial Systems.
Abstract: The computation of all solutions of a system of polynomial equations is a basic and in general hard problem.

The main techniques for accomplishing this task in an algorithmic manner, Grobner bases, multivariate resultants and continuation methods have received a great deal of **Scrooge Carol Essay**, attention recently. This thesis describes continuation methods for numerically determining all complex solutions of a system of polynomial equations. The emphasis is on the set up of **Undoing Trauma in Public Health Essay**, continuation problems which require as few paths as possible, rather than on **in A Carol Essay**, the numerical process of path following.
The key to efficient continuation methods is to realize the *Essay on The Being the Real* system to be solved as a generic element in a one dimensional parameterized family. **Scrooge Christmas Carol**? Polynomial systems which arise from practical problems usually have associated physical parameters, and are thus already presented as members of a parameterized family. In the first chapter we discuss the total space of such a parameterized family and its implications for continuation methods.

The main body of the thesis deals with the application of toric deformations, and polyhedral subdivisions to produce continuation methods which are optimal for systems with a given collection of support sets = _1. _ n . We identify monomials x ^ q = x _1^ q _1. x_n ^ q_n with lattice points q =( q _1. q _ n )in Z ^ n and allow polynomials of the form.
where i =1. **Undoing Trauma In Public Health**? n and the coefficients c _ i , q are complex. A famous result of Bernstein sates that, for generic choices of coefficients, the *Christmas* mixed volume of the Newton polytopes _ i = conv( _ i ) is equal to the number of isolated solutions in **alexander**, ( C *)^ n . In Chapter 2, the *in A* concepts of Minkowski addition, mixed volume, and fine mixed subdivisions are presented. The use of **the immoralist**, fine mixed subdivisions of the Minkowski sum _ i +. + _ n in computing mixed volumes generalizes the *Scrooge in A Christmas Essay* use of triangulations in volume computation. Computational techniques for computing mixed subdivisions via deformation are also described. In Chapter 3, these techniques are adapted to provide a constructive proof of Bernstein's theorem, as well as a generalization of Bernstein's theorem to counting roots in C ^ n . The algorithms described here have been implemented in a program called Pelican . Chapter 4 describes Pelican and **legacy** provides a tutorial and reference manual.
Algebraic K-Theory and Assembly for Complexes of Groups.
Abstract: I define the algebraic K -theory K_i(RG(X)) for a complex of groups G(X) and a ring R , incorporating the combinatorial structure of X as well as group-theoretic data. If G is the fundamental group of G(X) , I construct a comparison map K_i(RG(X)) to K_i(RG) and show that it is an isomorphism under certain geometric conditions on G(X) .
In addition I define an assembly map H_i(G(X);K(R)) to K_i(RG(X)) relating the *in A Essay* homology of G(X) to its K -theory. There is a natural transformation from the assembly map for G(X) to the ordinary assembly map for **Essay the Real** the group G, which is an equivalence when the above geometric hypothesis holds.

Normsets and Rings of Algebraic Integers.
Abstract: Let F be a finite field extension of K which is, in **Scrooge Carol**, turn, a finite field extension of Q , the rational numbers with rings of integers R and **review** T respectively. We will also make the assumption that T is a unique factorization domain. It is well-known that the norm function N_K^F from F to **Scrooge Carol**, K maps R into a multiplicative submonoid S of **Trauma Health Practice**, T which we will call the normset of R (with respect to T ).
Intuitively, the richer and more intricate multiplicative structure of the ring R could be lost in the translation to the normset. Much information, however, is retained in the structure of the multiplicative monoid S . **In A Christmas Essay**? It is the aim of this dissertation to investigate certain properties of the monoid S and deduce what those properties tell us about R . We will also ask what certain properties of R tell us about S .
In the first chapter, we investigate unique factorization properties. **Control Of Pain That**? There is *Scrooge in A Christmas*, a natural way to define the concept of unique factorization in the normset S . **Argument For Shakespeare Author**? The most important result of the first chapter is the fact that if K is Galois over F , then R has unique factorization if and only if S has unique factorization. We also define a more general class of fields where the unique factorization of S implies the unique factorization of R . In the second chapter, we look at the relationship between the class group of R and the structure of the normset will be investigated. **Christmas Carol Essay**? It will be shown that a property of a normset called saturation will measure how the Galois group acts on the class group, and from this some consequences about the structure of the class group of R can be deduced.
In the third chapter it is shown that in the Galois case, the normset determines the field extension. We also give an example of two non-Galois extensions such that the prime decomposition laws are identical, but the normsets are not.

In the final chapter, we use the *the immoralist* techniques of this thesis to prove some factorization results about orders in quadratic number fields.
Geometry and Combinatorics of Chow Forms.
Abstract: The Chow form of a variety is similar to a resultant. Given d +1 linear forms on a d -dimensional projective variety, the Chow form is a polynomial in the coefficients of the linear forms (unique up to multiplication by a nonzero constant) which is zero if and only if the *in A Christmas Essay* linear forms have a common zero on the variety. We can also express the Chow form in **the immoralist**, terms of the *Scrooge in A Essay* ( d +1) x ( d +1) minors of the matrix of coefficients.
This doctoral dissertation describes some of the combinatorial and geometric properties of the *harry harlow* Chow form of a variety. **Christmas Carol**? In chapter 1, we give an introduction to Chow forms and describe how to perform some basic geometric operations on varieties by manipulating their Chow forms. **The Gate Control Of Pain Suggests**? In chapter 2, we study the combinatorics of Chow forms of point sets in projective spaces and compare and contrast this theory with the theory of binary forms (which are Chow forms of point sets in P ^1).

We also consider the inhomogeneous version of this theory, the theory of multisymmetric functions . We give proofs for many of the *in A Christmas Carol Essay* assertions made in this paper, and also a counterexample to one of them. **The Immoralist**? In chapter 3, we consider the Chow polytope as a combinatorial invariant of the *Carol Essay* Chow form. **On The Argument The Real**? We show that the Chow polytope of the *Christmas* ruled join of two varieties (a construction used in intersection theory) is the Cartesian product of the Chow polytopes after a change of scale. We also investigate the *Essay Argument Being* stratification of the Chow variety of plane conics (whose points are the coefficient vectors of their Chow forms) induced by the different Chow polytopes. In chapter 4, we present a geometric algorithm for computing the Chow form of a ruled join in stages, and give examples of its use. Chapter 5 is somewhat disconnected from the remainder of the thesis; it proves that all connected complexes of coordinate lines in P ^3 are initial complexes of space curves. This is a partial converse to the cited result of Kalkbrener and Sturmfels that all initial complexes of irreducible varieties are connected. **Essay**? Appendix A describes some MAPLE code written by the author to implement the algorithms of Section 2.1.3 and to make it easier to execute the algorithm of **Essay Being**, Section 4.2.
Algebraic and Combinatorial Methods for Face Enumeration in Polytopes.

Abstract: Let P be a d -dimensional polytope and S a subset of d 1. We denote by f_S(P) the number of **Scrooge Christmas Essay**, chains of faces whose dimensions make up S . The flag f -vector is the vector made up of all such flag numbers. **The Immoralist**? This thesis studies linear and non-linear conditions on the flag f -vectors of **Scrooge Christmas Carol**, several classes of polytopes.
We define a noncommutative algebra whose elements can be viewed as linear forms of flag numbers of **harlow**, polytopes. By studying this algebra, we derive new proofs of the linear relations on flag f -vectors.

We also obtain results about the CD-index and symmetric linear forms having same value on any polytope and its dual. **Scrooge In A Christmas Carol**? We study linear equalities and inequalities on flag f -vectors of zonotopes. The method is to construct a class of zonotopes to establish a lower bound for the span of flag f -vectors. We also find a class of inequalities on **movie review**, flag numbers of zonotopes; some of the inequalities from this class do not hold for general polytopes. In the case of the cube, we prove the g -conjecture in a stronger form, i.e., the *in A Christmas Essay* generalized g -vector of cubes satisfy Kruskal-Katona inequality, which is stronger than the Macaulay inequality.
On Semi-Linear Representations Over Local Fields.

Abstract: In the theory of Galois representations, as the name implies, Galois groups are studied via their matrix representations. **Essay Being The Real Author**? In case the ground field is *Christmas Carol*, a p -adic field, the set of (continuous) representations of its absolute Galois group by integral p -adic matrices has the natural structure of a metric space. One of the *Historical Trauma Practice Essay* main results of this thesis is *in A Christmas*, that this metric space is bounded. Some related computations are given, describing the metric in **the butterfly movie**, detail for some special representations. Also discussed are some natural invariants of the *Scrooge in A Christmas* representations, and **movie** the extent to which they determine the representations.
The Semistability at Infinity for Multiple Extension Groups.
Abstract: Semistability at infinity is a geometric invariant used to study the ends of a locally finite, connected CW complex. **Carol**? One can use this definition to define the *the great* notion of the semistability at infinity for **in A Carol Essay** a finitely presented group. Much work has been done (especially by M. **Of Pain**? Mihalik) to show many classes of finitely presented groups are semistable. He has also given a definition of **Essay**, semistability for finitely generated groups that generalizes the original definition. He has used it successfully to show semistability for certain classes of finitely presented groups that are built up from finitely generated semistable subgroups.

It is unknown at this time whether or not all finitely presented groups with a finite number of ends are semistable at infinity. The purpose of this dissertation is to use this alternative notion of semistability for finitely generated groups and prove the class of finitely generated groups containing an infinite, finitely generated subnormal subgroup of finite index are semistable at infinity. This would generalize two earlier results of Mihalik. **Alexander The Great**? As a consequence, I will show the finitely presented analog of the main result.
A Combinatorial Geometry of the Whitehead Torsion of Finite Abelian Groups.
Abstract: Given an odd prime p and an arbitrary finite abelian p -group G , except for the exponent, not much is known about the invariants of the Whitehead torsion SK _1( Z [ G ]). Roger C. Alperin, R. Keith Dennis, Robert Oliver and Michael R. Stein have succeeded in **Christmas Carol**, using class field theory to give a simplified combinatorial description using norm residue symbols and the integral logarithm of **the immoralist**, L. Taylor and R. Oliver.
In this thesis, inspired by **Christmas Carol** the delicate explicit calculations of specific groups by Oliver, we attempt to develop a combinatorial geometry that may facilitate a better understanding of the *alexander* complications involved in these computations. Chapter 1 introduces cocyclic homogeneous functions, and explains how they relate to the existing theory. Chapter 2 builds the *in A Christmas Essay* combinatorial machinery that is relevant to the calculations in **study**, this essay.

The resulting geometry seems to borrow the notion of **Scrooge Carol Essay**, a tree from graph theory, and amalgamate it with the idea of a characteristic function from analysis! Chapter 3 should convince the reader that this geometry is fruitful; for even with rather crude tools, one can exploit the transfer homomorphism to deduce useful conclusions for a large class of SK _1.
In Chapter 4, we bring this geometry to focus on G simeq ( Z _ p^e )^2 and calculate explicitly the top rank in addition to other results. The main difference between the *Historical Trauma in Public Health Essay* approach of **Christmas Carol Essay**, Alperin-Dennis-Stein and ours is that instead of using the full flexibility in the choice of representatives of the *the gate theory suggests that* orbits in the character group of G , we specialize to one particular choice. **Scrooge Carol Essay**? We close the essay by debunking a hitherto hope that monomorphisms of **the immoralist**, finite abelian p -groups should induce monomorphisms on the SK _1's.
Explicit Weight Two Motivic Cohomology Complexes and Algebraic K-Theory.
Abstract: Beilinson et al.'s Motivic Cohomology Complex is related to a motivic complex (considered earlier by Lichtenbaum) formed using groups related to the scissors congruence groups. **Scrooge In A Christmas Essay**? This involves an algebraic study of configurations of lines in **harlow study**, projective space.

One thereby obtains a more precise relationship between the cohomology of **Christmas**, Beilinson's complex and **effect movie** lower dimensional K -groups. Most of the proofs omitted in Beilinson et al. are supplied here. There is also a list of certain torsional elements of the third K -group for fields between the rationales and the real cyclotomics. The relevant key words are: Aomoto, polylogarithm, torsion in K _3, scissors congruence group, configurations of lines in projective space, motivic cohomology.
Combinatorial Structure on **in A Carol**, the Hilbert Scheme.
Abstract: In this thesis, the component structure of the Hilbert scheme is *the butterfly movie*, investigated.

The techniques used to **Scrooge Christmas**, carry out *harlow*, this investigation include Grobner bases, state polytopes, Hartshorne's fans, normal bundles, Borel-fixed ideals, and **Scrooge in A Christmas** methods from deformation theory.
Signed Sequences and Rolle's Restrictions: Why Not All Real Differentiable Functions and Polynomials Satisfying Rolle's Theorem Are Constructible.
Abstract: We investigate which sign sequences can be generated by a single univariate polynomial, and show that there are restrictions other than Rolle's theorem on polynomials. **The Great Legacy**? We then prove a fifth order Rolle's theorem, showing that an arrangement of roots satisfying the *Essay* classical Rolle's theorem is not constructable by a real differentiable function.
Rewriting Systems for Coxeter Groups.
Abstract: A finite complete rewriting system for a group is a finite presentation which gives a solution to the word problem and a regular language of **the butterfly effect movie review**, normal forms for the group. In this thesis it is shown that the fundamental group of an **Christmas Essay**, orientable closed surface of genus g has a finite complete rewriting system, using the *the gate control theory that* usual generators a _1. a_g , b _1. b_g along with generators representing their inverses. Constructions of finite complete rewriting systems are also given for any Coxeter group G satisfying one of the following hypotheses.
1) G has three or fewer generators.
2) G does not contain a special subgroup of the form s_i, s_j, s_k | s ^2_ i = s ^2_ j = s ^2_ k = ( s_i s_j )^2 = ( s_i s_k )^ m = ( s_j s_k )^ n =1 with m and n both finite and not both equal to two.
Endomorphisms of Negatively Curved Polygonal Groups.

Abstract: The theory of automorphisms of free products with amalgamation is well-understood. We examine the dimension 2 analogue of a free product with amalgamation, a polygonal amalgam, and show that in general the *Scrooge in A Carol* automorphisms of polygonal amalgams are similarly well-behaved.
Special Values of L-Functions of Curves Over Finite Fields.
Abstract: The central theme is to establish an **the gate control suggests**, equality L = chi, relating the value of L -function to an appropriate Euler characteristic. The first chapter studies various cohomologies, giving the definitions of the *Scrooge Essay* Euler characteristics and proving necessary properties. The second chapter uses lambda-adic cohomology to compute values of L -functions and proves the main theorem.
Groups of Piecewise Linear Homeomorphisms.
Abstract: Given a compact subinterval of the real line, the order preserving piecewise linear homeomorphisms of the interval form a group under composition. In this thesis we study subgroups of such groups obtained by restricting the slopes and singularities occurring in **Argument for Shakespeare the Real Author**, the homeomorphisms. We also consider analogous groups of **Christmas Carol Essay**, homeomorphisms and bijections of the circle.
This class of groups contains examples which have furnished the first examples of finitely presented infinite simple groups.

We extend this by exhibiting simple subgroups in all of these groups, and showing them to be finitely presented in some cases.
We then consider subgroups obtained by restricting slopes to a finitely generated subgroup of the rationals generated by integers, say n _1, n _2. n_k , and insisting that the singularities lie in Z [1 / ( n _1 n _2. n_k )].
We construct contractible CW complexes on which these groups act with finite stabilizers, yielding classifying spaces as the quotients. We obtain combinatorial information about the *the butterfly movie* groups by studying these classifying spaces. **Carol**? We compute homology and **Health** obtain finite presentations.

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amy edwards resume Quality, Responsive and Trustworthy Family Law Services. We offer clients a strong work ethic combined with prompt and personalized client care. Everyone must eventually face death, whether it is their own, a loved one, or that of their estranged spouse or a former spouse. *Christmas Essay*. In family law, it is no different. As it must, the **of pain** law accounts for these contingencies.
Although most people don#8217;t think that much about it, just like a marriage, a death impacts many family rights and **Scrooge in A Christmas Carol**, obligations. While family laws address death, it is an *Undoing Historical Trauma Health*, area of the law that intersects with inheritance laws. This article focuses on the North Carolina family law perspective. *Scrooge In A Carol*. Upon the **the immoralist** death of a spouse, the legal status of the surviving spouse automatically becomes widow or widower. This is a legal status used to determine all kinds of rights, including certain retirement benefits, social security, real property (depending on in A Christmas Carol Essay, how the deed is drafted), and even the right to *legacy*, obtain sensitive documents from the North Carolina Vital Records.

Those who are widows or widowers also receive certain military benefits, such as being eligible for **Christmas** interment at a State veterans cemetery, payment of a death gratuity and the right to access otherwise restricted military discharge records.
NC Gen. Stat. 65-43.1 and NC Gen. Stat. 47-113.2. A widow also has the right to apply to the clerk of harry, court to resume the use of her maiden name, the name of a prior deceased husband, or of a previously divorced husband in the case of a widow. A widower also has the **Scrooge Christmas Carol** right to apply to the clerk to resume the use of his premarriage surname.
NC Gen. Stat. 101-8. Widows or widowers may have the right to file certain lawsuits, such as wrongful death, including loss of consortium, or emotional distress, against a third party based upon the death of the other spouse.

Perhaps the most fundamental issue of all is who has the authority to dispose of someone#8217;s remains. An adult has the right to #8220;authorize the type, place, and **harry**, method of disposition of the individual#8217;s own dead body#8221; by funeral or cremation contract, a healthcare power of attorney, a written will or other statement signed by the individual and **Scrooge Carol**, witnessed by two persons who are at least 18 years old. Service members and certain federal employees may appoint the #8220;person authorized to direct disposition#8221; by using a Department of Defense DD Form 93. If the deceased person did not use any of the above methods to express his or her desire related to the funeral and disposal of his or her remains, the surviving spouse #8220;may authorize the type, method, place, and disposition of the decedent#8217;s body.#8221; NC Gen. Stat.
130A-420. This assumes no contract such as a prenuptial agreement or separation agreement has been executed that provides otherwise. There are special rules for Native American remains determined to be antiquities.

When a parent passes away, the surviving parent is automatically the sole custodian of the child unless there are extraordinary circumstances, such as when a court has terminated the rights of that parent. Children are usually entitled to social security benefits as a result of the death of that parent. *The Immoralist*. If a married person wants to adopt a child, North Carolina requires both spouses to sign the **in A Carol Essay** adoption petition. *Argument Being The Real Author*. If an adoption petition has been filed before the death of one of Essay, them, the court may still enter an adoption decree listing the deceased party as a parent, essentially allowing him or her to adopt the child after death. The adopted child is then legally treated as the natural born child of the deceased party for the purpose of Undoing Trauma in Public Health Practice Essay, inheritance.

NC Gen.
Stat. 48-2-204. *In A Christmas Carol Essay*. If paternity of a minor child is disputed after the death of a suspected biological father, in certain situations, the law permits biological testing of the child and the deceased man to determine whether he is the biological father. If the court rules that the deceased person is in fact the biological parent, the court must #8220;backdate#8221; any decree of paternity to indicate paternity before the date of the death. NC Gen. *The Immoralist*. Stat. 49-14. *Scrooge In A Christmas Carol Essay*. It is a crime after the twentieth week of a woman#8217;s pregnancy #8220;to advise, procure or cause a miscarriage or abortion when the procedure is performed by **alexander legacy** a physician licensed to practice medicine . . .#8221; unless #8220;there is substantial risk that continuance of the pregnancy would threaten the life or gravely impair the health of the woman.#8221; See NC Gen.
Stat. 14-45.1. It is a felony to *Christmas Essay*, conceal the **alexander** birth of a child #8220;by secretly burying or otherwise disposing of the dead body of Carol, a newborn a child #8220;by secretly burying or otherwise disposing of the dead body of a newborn child.#8221; Anyone #8220;aiding, counseling or abetting any other person in concealing the birth of a child . . . shall be guilty of a Class 1 misdemeanor. *Control Suggests That*. NC Gen.

Stat. 14-46. *In A Christmas Carol*. When there is what the **the immoralist** law calls a #8220;spontaneous fetal death,#8221; either parent may file an application requesting a #8220;certificate of Scrooge Essay, birth resulting in *the immoralist* stillbirth.#8221; The certificate #8220;shall not include any reference to the name of the stillborn child if#8221; the death report doesn#8217;t list one, and one is not listed by the parents. Any such certificate #8220;shall clearly indicate that it is not proof of Christmas Essay, a live birth.#8221; NC Gen. Stat. *Control Theory Of Pain Suggests*. 130A-114. A person who unlawfully causes the death of an unborn child is **in A Christmas Essay**, guilty of the separate offense of murder of an unborn child if that person willfully and maliciously takes some action with the intent to cause the death. Along with a few other situations, the crime is also committed if the person who causes the death is doing something #8220;is inherently dangerous to human life and is done so recklessly and wantonly that it reflects disregard of Historical Health Practice, life.#8221; NC Gen. Stat. 14-23.2. Download documents or make a payment here.
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View or join our mailing list here. Welcome to Our Family Matters Archive Page. To read our family law blog, click here. 2017 Amy Edwards Family Law. All Rights Reserved.

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Easy Words to Use as Sentence Starters to *Scrooge in A Christmas Carol Essay* Write Better Essays.
VirginiaLynne has been a University English instructor for over 20 years. She specializes in harry helping people write essays faster and easier.
Word or phrase used at the start of a sentence to *in A Essay* show the relationship between ideas.
Can you quickly and easily improve your writing?

Yes. For over on The Argument 20 years, I've been teaching the tips I share below to *Scrooge in A Christmas* my students and every time they apply these tips, their writing gets dramatically better. **Essay For Shakespeare**. Why? Three reasons:
These tips and transition words help you resist the old habit of simple subject-verb sentence structure and develop richer and more nuanced ideas. By adding transitions to your sentences, you link your ideas more effectively. These words make your writing sound more professional and less like spoken language.
How To Use Sentence Starter Lists.

The most important tip for **Scrooge in A Carol** improving your writing quickly is to *the immoralist* follow one rule:
Start every sentence in a paragraph with a different word. How? Here is my step-by-step guide:
Use the transition list as you write: Think about how the sentences in your paragraph are related to *Christmas Essay* one another. If you are comparing and suggests that contrasting two ideas, then use the Showing Contrast transition words (see list below). Are you writing about steps in a process? Then use the Adding to *Scrooge Christmas* an Idea transition words below. When writing about something that happened, use the Sequence/Time transitions I've provided. Using the transition list while you are revising : Sometimes, it is *the gate control* easier not to worry about these words until your final draft stage, especially if you are a beginning writer. **Scrooge In A Essay**. How do you do this?

Use the **the butterfly review** following tips: Go through your first draft and circle the **Scrooge in A Carol** first word in every sentence. If you use the same word to *the immoralist* start a sentence twice in a paragraph, then you need to *Christmas Essay* choose another transition word and effect movie re-word the sentence. How to *Scrooge Essay* choose transition words? Think about how each sentence fits with the one before it.
Does this sentence add information? Then use moreover, furthermore, or another word that adds to *movie* the idea.
If this sentence contrasts with the previous sentence, you might use however or on the other hand.
If it is a time sequence, use next, then, or consider using first, second, etc.
Dont use the same transition too often. Also, don't forget the comma after the transition word and in A Carol don't forget to *effect review* put the subject of the **Scrooge Christmas Essay** sentence after the comma.

What makes using transitions improve your writing is that it forces you to explain the connections between your ideas. Ask yourself:
What does the sentence before this one say? How does this sentence relate to *on The Argument the Real Author* that one? Scan the list for a transition that seems to fit best. You can also use these questions for **Christmas Essay** help:
Does this sentence add information? Then use: moreover, furthermore, additionally, or another addition transition.
Does the sentence contrast or contradict? Use: however, on the other hand, in contrast, or another contrasting transition.

Are you writing something that happens in order? Use: next, then, or consider using time order like first, second,etc.
Does this sentence add evidence? Use: for example, consequently, for this reason, or another consequence transition.
Does the sentence emphasize an *control suggests*, idea? Use: obviously, especially, as a rule, particularly or another emphasizing transition .
1. Use a variety of transition words, not the same one.
2. Put a comma after the transition word.

3. Put the subject of the **Scrooge in A Essay** sentence after the comma.
2. Use a Variety of Words When Citing Examples.
3. **Trauma In Public Practice Essay**. Use Different Words to Order Events and Sequence Time.
4. Use Interesting Words When Summarizing.
Short paragraph without transition words:
Cell phones have changed our family communication for **Carol** the worse. Parents complain their teenagers spending too much time on their phone.

Teenagers are annoyed that they can't get the attention of their parents who are always working or shopping on their phones. **Essay On The For Shakespeare The Real**. We need to make some changes.
Generally speaking, cell phones have changed our family communication for the worse. Obviously, parents complain about their teenagers spending too much time on their phones. Moreover, teenagers are annoyed that they can't get the **in A Christmas Essay** attention of their parents who are always working or shopping on their phones. Unquestionably, we need to make some changes.
Just following my tips to *alexander* add transition words to your essay can often make your essay much better and will probably improve your grade. Inevitably, as soon as I tell my classes about **Scrooge in A Christmas**, this technique their writing improves dramatically. Better yet, the more you use transition words in the butterfly effect review revision, the more you begin to add that technique to *Scrooge* your writing during the first draft.
Why does that help? It begins training you to think about how your ideas relate to one another and helps you to write essays that are deeper, more connected and logical.

If you've found this technique helpful, or if you have another sentence starting technique, please add your comments below to help out other writers. How many times to you revise an essay? Sentence Starters for Reader Response Essays and Journals. by Virginia Kearney 6. 9 Simple Steps to Improve Your Writing. by kbdressman 2.

Flash Fiction: Genre Facts, Writing Tips, and Being the Real Stories. by Linda Crampton 72. Easy Argumentative Essay Topics for College Students. by Virginia Kearney 5. 100 Problem Solution Essay Topics with Sample Essays. by Virginia Kearney 42.

How to Write a Proposal Essay/Paper.
by Laura Writes 40.
Virginia Kearney 8 hours ago from United States.
Hi Harni--I have lots of help for writing essays of all sorts. Just follow the **Scrooge in A Carol Essay** links to the side of this article, or look at the links to different kinds of essays on my profile page.
This helped me sooo much Thank You.
I was just wondering how to start an essay like the introduction.
Virginia Kearney 22 hours ago from United States.
Hi Ryan, You can use any of the words here in front of the **effect** I or you can use a phrase from the end of the sentence. Here is an example:

I am going to the store because I need to buy groceries.
Because I need groceries, I'm going to *Scrooge Essay* the store.
Frankly, I need groceries, so I'm going to the store.
Hi, I was just wondering easy ways to replace I at **effect movie review**, the beginning of Scrooge in A Carol Essay, a sentence. Sometimes, I struggle with this, and the replacements I find sound unnatural.

This is a great article though.
Virginia Kearney 8 days ago from of pain suggests, United States.
Hi Sepphora, you want to *Scrooge Carol* start by underlining all the first words in your sentences. When you find you are using the same word to start a sentence (especially in harry the same paragraph) you should use one of Scrooge in A Christmas, these ideas instead.
my problem is the different word to use or replace .
This helps me so much.
Virginia Kearney 2 weeks ago from United States.
Hi Mimi--To avoid the passive sentence, you want to put the **on The Argument Being the Real Author** actor first. In your example, one way to fix this is to ask who considered Mimi? Then instead of Christmas Carol Essay, was given consideration you would use the more direct considered.

Example: The orchestra director considered Mimi for the position of first chair but thought she would be too nervous.
How do you write non-passive sentences? For example, Mimi was given consideration.
thank you very much, it really helped me :)
Already bookmarked it. **Harry Harlow**. This article helped me for my entire 2 years masters. Thanks a lot for **Scrooge Essay** writing such informative post. Also, do write update us with more of this awesome posts.
Thank u very much ,the info really created an impact in my essay writing.

Thanks it really helps me while writing.
I'm very thankful for this article. It really helps my essay.
Great advice well laid out.
Awesome Article, no words for your well-crafted words.
Virginia Kearney 2 months ago from United States.
Hi, Thomas--I'm glad you asked. I have over 100 articles to help people improve their writing, including ideas for **the butterfly review** proofreading your own essay and Christmas Carol questions you can use to have other people evaluate your essay to help you improve your writing.

I also have an *the great*, article on effective sentences and grammar help for using punctuation marks. You can find these articles by looking at my profile page or following the links on the side with my name. In working with non-native writers, I find the most important editing technique is to have several people look at your essay carefully and to read the **in A Christmas Carol** essay out loud as you proofread. My final best tip is to *the immoralist* focus on one or two rules a time as you go through the **in A Christmas Essay** paper. Then you can make sure that you have corrected for that error carefully. Hopefully, your instructor can help guide you to know which rules are most important for **the immoralist** you to *Christmas Carol Essay* focus on *the butterfly effect movie review*, first. I'm afraid I don't know of any websites where you can submit your work to get help.
Hey, great article!
Do you have any suggestions for non-native english speakers that are working on an english essay? Especially regarding proof reading?
Are there any platforms where one can get help from others?

Virginia Kearney 2 months ago from United States.
Hi Mahmoud! I have over 100 articles on writing that are published here on *Scrooge in A*, Letterpile. **Effect**. You can find help with grammar and also on how to *Christmas Carol* structure sentences and essays. Look at my profile or follow the links to the side that have my name.
Thanks.

That was great and the gate theory that useful. Since I'm not a native i encounter with more problem than you mentioned what i am gonna do? Absolutely amazing tips! Nice article Virginia, I have gained from Scrooge Essay, it a lot especially the transition words. being a newbie at content writing this article helps. Hi Virginia Kearney, Thank you so much for the quick response.

Virginia Kearney 5 months ago from United States.
Hi, Himabindu- So, is generally used as a coordinating conjunction (others are and, but, or, and yet) and therefore would generally not be used correctly to *alexander legacy* start a sentence, but rather as a way to *Scrooge* join two sentences. Example:
The bookstore didn't have what we wanted, so we went elsewhere.
However, in your example, you are using so as an interjection in a conversational style sentence. You could vary this by saying:
Actually, I don't.
In reality, I don't.
Furthermore, I really don't.
The truth is that I really don't.

In the second example, you are using as in an introductory phrase, which is another way to vary your sentences besides just using a sentence starter transition word. When you are trying to decide how to write a sentence differently, you need to decide what that sentence is *harry study* doing. Is it adding to what you've already said? Then use words like Additionally or Furthermore. Is it contradicting or changing the direction? Use However, In contrast or On the other hand. In your two examples, you are talking about the cause, so the best choices are Because, Since:
Since this book is not useful to me, I really don't want it on *Essay*, my shelf.

Because this book wasn't useful to me, I don't want it on my shelf.
You can also vary the meaning a bit with sentences like this:
In general, this book wasn't really useful to me, so I don't want it on my shelf.
hi.. this post is very useful. If I have to use transition words that means, 'so' or 'as' or 'that's why' what I have to use? For example, I say So, I don't want to use this in my book or As this book is *legacy* not useful to me, I don't want to see this on my shelf. **Scrooge In A Christmas Essay**. If I have to say the **harry harlow** same sentences in a different way, how can I say?
Fatima Roque 5 months ago.
Thank you so much, this will help me in my IELTS preparation especially in writing and Christmas Essay speaking as well. **Control Of Pain**. :)

Ronald Cole 5 months ago.
This information has helped me a great deal. I have never been one to write much using transition words has always been a weakest.
Virginia Kearney 5 months ago from United States.
Hi Hannah Baker, I'm so glad to *Christmas Essay* hear that you are writing a book.

My teenage daughter is also a writer and I think it is *harry study* really wonderful that anyone can now write something and post it online for others to *Scrooge Carol Essay* read. I might have become a fiction writer if that had been available to me as a teen. Thank you for spending the time to know that I've helped you. I teach college students but I have found many younger people are also looking at **harry**, my articles and I'm thinking about creating some information just for them. **Scrooge Carol**. I'd love to hear what younger people want to know about how to write better.
Hannah Baker 5 months ago.
My name is not really Hannah Baker though, just a cover up. I'm a teen I and love writting. I'm recently stuck on *harry study*, a book that I'm writting, called The Chosen One, and I was getting for frustrated because I kept using the same words or phrases. I ended up finding this website and in A Christmas it really helped me, so thank you very much.
Virginia Kearney 5 months ago from United States.

Hi Jodah! I'm often trying to force myself to use some new transition words in my writing as well. Along with the words I put in the immoralist this article, you can also use different kinds of phrases at the start of a sentence. I especially like gerund phrases like Walking down the street, Thinking about my children, or Writing in a new way.
John Hansen 5 months ago from Queensland Australia.
This is very helpful Virginia. I never start sentences in a paragraph with the same word, and do use transition words, but I probably only use the **Christmas** same favourites over the immoralist and over (about 10) as you mentioned in your comment to Bianca.
Solved my biggest problem as I always tend to use same transitions again and again in a paragraph. Thanks, I appreciate your effort.
this really helped thanks.

Virginia Kearney 6 months ago from United States.
Bianca--I generally find the adding and Scrooge in A Christmas contrasting words are the most useful for me. **Of Pain**. In fact, I think that when you start to use this technique that most people pick 6-10 favorite words and use them most of the **Essay** time.
Bianca di'Angelo 6 months ago.
Thank you for this. I'm writing an essay on how advertising affects youth but I keep needing to pause every few words to try and find just the right one. Another or additionally. overall or in conclusion. I think the most helpful ones for **Trauma in Public Essay** me were the words to add ideas.

This is a lifeline for **in A Carol Essay** me.thank you.
Virginia Kearney 6 months ago from United States.
Michaela--Whether this will work as a subject for **the immoralist** your paper depends on *Scrooge in A Christmas Carol Essay*, your assignment. You could do legends about elves and find evidence on that.
Virginia Kearney 6 months ago from United States.
Hi, Liv-I have two articles that could help you. One is *the butterfly effect* about writing a thesis sentence and the other is about writing topic sentences in paragraphs. Often, these sentence starters can be used to *Scrooge in A Christmas* write better topic sentences because they can help you link your ideas and for Shakespeare show how one topic sentence either adds or contrasts to the ideas before.
I don't understand how to start the topic sentence of the **Scrooge in A Essay** paragraph, so I suggest that this page should include starting words for topic sentences in effect paragraphs.

Jorge Oliveira 7 months ago.
Thank you so much for showing me how to use transitions with accuracy!
Kendall Kincaid 8 months ago.
Thank you for **Christmas Carol** the help!
Kayla Miller 8 months ago.
Thank you soo much for the Article!

That will come in handy in harry study writing assignments.
Russell Morrison 8 months ago.
Reading this has given me some new words to *Scrooge* start my paragraphs with. Thank you!
This helped me improve my writing.Thanks :)
wrong your all wrong im a book writer 9 months ago.
your all wrong im a book writer.
Thanks soo much I have be having the **Essay for Shakespeare** worst time with passing my essay for a state board exam and I am going to use your effective strategies to make some improvements.
Virginia Kearney 9 months ago from Scrooge Christmas Essay, United States.

Hi Daniel--Transition words like these sentence starters are used as the first word in a sentence. Often, they have a comma after them, just as I show in movie review this sentence. Here is a sample using some really simple sentences:
Global warming is increasing. Scientists say ice caps are melting quickly. **In A Christmas Carol Essay**. The CO2 levels around the world are much higher than just fifty years ago. We need to *legacy* do something now.
With transition words:

Unfortunately, global warming is increasing at a rapid rate. In fact, scientists say ice caps are melting quickly. Additionally, the **Scrooge Christmas Essay** CO2 levels around the world are much higher than just fifty years ago. With this in mind, we need to do something now.
I have a question. I don't understand how to use transitions still and my paper is due after Winter Break. Please help?
Virginia Kearney 9 months ago from United States.

Hi Dustin! I'm happy that my work has helped you. **Essay For Shakespeare Author**. Please check out *Scrooge Essay* my other articles on *alexander the great legacy*, different types of essays for more help.
Thx this helped me out for **Christmas** my essay you will be the **Being** only site I will use .
Awesome article, I printed it out to use as a reference.
Venkatachari M 11 months ago from Hyderabad, India.
Very useful article for improving one's style of writing. Thanks for sharing this wonderful knowledge.
This is *Scrooge in A Christmas Essay* a good website for kids.
Thanks u helped me with my assignment.
Emily 12 months ago from Oregon.
I love the charts; they really lay things out concisely.

Thanks for the helpful information. I'm glad to add another specific tool to my writing toolbox!
Virginia Kearney 12 months ago from United States.
Sirin, It is *the great legacy* optional to put a comma after a short transition or introductory element. For example, I can put a comma in this sentence after example but the meaning is clear if I don't, so it is all right to leave the comma out.

However, you are not wrong to add the **Scrooge Carol** comma and it often makes the sentence clearer. Here are some examples and you can decide whether the comma is *Trauma in Public Health Practice Essay* helpful or not:
Nevertheless, I believe she is correct in her assumption.
On the other hand, what they think is also correct.
Hello,you said that it is important to put a comma after each transition word,but i found in a book i have read that, of Macdwell about British history,he uses no commat after each transition he put.I want to know please :is this permmited in Scrooge Christmas writing or no.And,in the same time, we can't say he is *theory of pain that* wrong since he is an auther and Christmas Carol he publishes books.thank you in advance.
Virginia Kearney 13 months ago from the butterfly movie, United States.
Hi, Ahmed!

To go to a new idea, you could use a contrasting transition, such as on the other hand, or however. It might be possible to use the sequence transition words first, next, etc. **Scrooge In A Carol**. if you are doing something that happens in time or in the immoralist space. If you are adding a new idea to support the main point, then you can do additionally, moreover or in fact.
Interesting, but which words used to start new topic / idea .
thank you so much for doing this it helped me a lot and I'm sure I'll be visiting this page in the future.
Virginia Kearney 13 months ago from Christmas Carol, United States.

Congratulations on starting to *control theory that* learn English, Maria! I have almost 100 articles to help you and there are other writers on HubPages who have articles especially for ELS learners. Good luck! Learning English takes work but I know you can do it!
I'm beginners .I wanna to *Scrooge in A* learn English as second language .
Ithink these words help me a lot.
Omg this helps/helped me so much with writing my essays.So happy I found this website and thank you for **alexander the great legacy** creating it.
Virginia Kearney 14 months ago from United States.

So glad this helps you Jackie. Check out *in A Carol* my other articles for even more help and ideas! Every year, I get more ideas from my students to incorporate into my site. Teaching is always about **Historical Health Practice Essay**, learning as well as giving out *Christmas Carol* information.
Brilliant, I have hit a plateau tonight writing an assignment for **Argument for Shakespeare Being Author** uni, and now this has given me a whole heap of in A Christmas Essay, ideas.
John Hansen 15 months ago from Queensland Australia.
Very professional article, Virginia. Your wise advice and list of words is very helpful.

Thanks for **the immoralist** this post it really helped me.
Virginia Kearney 16 months ago from United States.
Tina--thanks so much for your comment! I'm always so happy when someone tells me that what I've worked so hard to put together has helped them learn to *in A* write better. Now that all of us communicate so much through the **the gate control** Internet, I think learning to write clearly is even more important than ever.
Tina Kozma 16 months ago.
This website is the only website I use when writing essays. In fact, I have this website on my desktop so I can easily access it. Thank you so much for putting this information together!

Asher Socrates 19 months ago from Los Angeles, CA.
This is a very informative and helpful write up with straight to *Scrooge in A Christmas* the point instructions. I will be book marking this to help me break away from my many bad habits when it come to *control theory suggests that* writing. Thank you very much!
This really helped thanx.
Virginia Kearney 20 months ago from Scrooge Christmas Carol, United States.
So glad that you think these will help your friend JG. I have a lot of second language readers. I've taught students from many different countries and, in fact, that is how I've come up with some of my material. I would see something that my students were having trouble doing and then tried to figure out *on The Being the Real* a way to help them write better in that area.
jgshorebird 20 months ago from Southeastern U.S.

Great information. Not that I am any good, but I have a friend who is having trouble in college (she is Spanish -- having a difficult time) and your hubs are a gold mine. **In A Carol Essay**. Thanks.
Thank you so much. This will help me with my AP class. (:
Virginia Kearney 21 months ago from United States.
Thanks so much! All of Health, my articles were written first as notes for lectures for my students.

They are the ones who taught me what students want to know. My whole goal is to make writing easier and more accessible. I'm especially glad when it helps English learners from other countries.
Kamaraju Pulugurtha 21 months ago from Christmas Carol Essay, Khammam, India.
I like this Post, mainly it doesn't sound look like a Page out of a Grammar Text, creating a feeling of horror. **Essay Being The Real**. I find it hospitable, offering bits and bits of advice.

Virginia Kearney 2 years ago from Christmas Carol, United States.
The idea for this list was one I was given by an older professor when I was in graduate school. It was definitely some of the best advice I had ever gotten about writing. I love the fact that the idea is *harlow* so simple but it really makes a huge difference in the sound of a person's writing. **In A Essay**. I've added a lot of words to the list over the years and added the rules of how to use these in sentences.
This post is *Health Practice* very helpful and practical! I have often struggled with starting sentences the same way and I think this will make me a much better writer.
This is great information. I cannot count how many times I have been stuck using the **Scrooge in A Carol** same starter over an over and wishing I could add more variety to my writing.

Extremely helpful ideas and lists of words.
Gary Malmberg 2 years ago from Trauma in Public Health, Concon, Chile.
Love this. **In A Essay**. I'm saving it for **the gate control theory of pain suggests that** the future. Two thumbs yup.
Cheryl Simonds 2 years ago from Connecticut.
Great hub! The reference lists are going to *Scrooge Carol Essay* be a favorite of harry, mine from now on.
Very helpful hubs, I will certainly use transitions words in all my further revisions.
Virginia Kearney 3 years ago from United States.

Just Rodney--You are right about the differences in language. **In A Christmas Carol**. What I teach at my University is standard American English. Since I was born and raised in California, I speak and write in the great the standard dialect of the U.S. movie and T.V. culture, which has become standard English in America through that medium. One of the **in A Carol** reasons that English has become such a universal language is that it is very adaptable and tends to allow people to add words from other languages, as well as add different ways of expressing thoughts. I now live in the Southern United States and love some of the different expressions here.
Rodney Fagan 3 years ago from Johannesberg South Africa, The Gold Mine City.

Well written Hub, although English is spoken and written in a vast number of Countries; there are various grammatic, spelling and other subtle usages that come into play!
RTalloni 3 years ago from the short journey.
As always, great stuff from you. **The Immoralist**. I enjoy your hubs and like learning from them. The comments here reflect the usefulness of your work to *Scrooge* a wide range of readers.
Virginia Kearney 3 years ago from United States.
Thanks Lynette! I'm so glad you are working for **Undoing Health Practice Essay** your GED. It is not easy to *Scrooge in A Christmas Carol Essay* finish everything but it will certainly be worth it.

Lynette Scott 3 years ago.
I have just been given your list in my GED class. Quickly browsing the article, I am sure it will help my sentence structure. **The Great**. Here is one suggestion I would like to *Carol* add for **alexander** you.
Use Remember, instead of Don't forget,
As in from your article Remember, the comma after the **Christmas Carol** transition word, and remember to put the subject of the sentence after the comma.
Virginia Kearney 3 years ago from United States.
Hi Jade--Your example shows another way of starting sentences effectively, and that is by *effect movie* using a descriptive phrase. From reading your comment, I'm guessing that English is *Christmas Carol Essay* not your first language because the way you have phrased your sentences is *the butterfly effect movie* not quite correct for **in A** a native speaker.

However your point is excellent. Instead of the great legacy, putting the subject first in a sentence all the **Scrooge Christmas** time (which English speakers generally do when talking because that makes the meaning of the sentence clearer), you can put a descriptive phrase or even part of the predicate of the sentence at **control**, the beginning. I will reword your sentence a bit to make it more correct in standard English:
One bright, sunny summer day, the **in A Carol** son shone brilliantly through the **the immoralist** clear class window.
Here are some other examples (notice how these short sentences jump out!):
Flashing an *Carol Essay*, angry eye at **of pain suggests that**, me, the horse ran quickly past and Christmas Essay jumped over a fence.
Darting about the flower, the bee finally settled down to *harlow study* gather some pollen.
It's really good, but on the other hand you should add more sentence starter like: One bright sunny summer day the **Scrooge in A Carol** sun shone on the glass clear window. **Movie**. Also do you think that was good?

Virginia Kearney 3 years ago from United States.
Glad to know this helped you Daily--I find that my students start writing better immediately when they use this list.
Virginia Kearney 3 years ago from United States.
So glad to *Scrooge Essay* know this helps you devsmilez. I always teach this to my classes as a quick and easy way to improve your essays. I see dramatic improvement when students use these.
Joey Keefe 4 years ago from Albuquerque, New Mexico.
Interesting article. Using transition words like the ones you listed can be a great way to start a sentence. However, I've noticed in my own writing I can fall into the habit of effect movie, using transition words as a crutch.

So while I definitely agree that transition words are useful and Scrooge Essay effective, they can spoil an otherwise good piece of alexander the great legacy, writing if used too flippantly. AngPow 4 years ago from North Cali. Wow. Thank you for the list of transition words, VirginiaLynne. This hub will help a lot for the multiple essays and papers that I have to write this semester.

Thank you for sharing.
I have to *Essay* write an *review*, essay on sports and my first paragraph has to include the author, title, publisher, etc, as well as a summary of the **Carol Essay** main points and ideas. I cannot figure out how I should start this essay. **Trauma In Public Practice Essay**. Please help!
Virginia Kearney 4 years ago from United States.
Good point Tex. What emphasize in my class is that you need to pay attention to how your ideas connect with one another. Usually you are adding, contrasting or comparing. Transition words help you make that distinction clear.

In spoken language we often use tone, voice and gestures to make those connections, but in written language we need to use transition words and in A Christmas punctuation.
texshelters 4 years ago from Mesa, Arizona.
Certainly, paying attention to *harry study* transitions is important. However, when a writer uses a transitional phrase or word just because they should and not because it fits, the **Scrooge in A Carol** writing can come out even worse.
Virginia Kearney 4 years ago from United States.

Good question aya. **Essay On The Argument The Real Author**. Here are some ideas: On Saturday and Sunday; add another transition word like, Sometimes on the weekend; change the on to another transition word like During the **in A Essay** weekend; switch your sentence around so that on the weekend comes at the end, such as We love to go sailing on the weekend instead of the gate, On the weekend, we love to go sailing; and try a variation like Weekends. Hope that helps!
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