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THEMATIC PROGRAMS
March  1, 2012
Fall 2005
Renormalization and Universality in Mathematics and Mathematical Physics
Spring 2006
Holomorphic Dynamics, Laminations, and Hyperbolic Geometry
Dynamical Systems Seminar
Mondays, 3:10 p.m. Room 230
Audio of talks available here.
May 31, 1:30 p.m.
** (Note special time)
Hui Guo (Fields Institute)
Integrable Teichmuller spaces
We introduce a new kind of subspaces of the universal
Teichmuller space. Some characterizations of them are given in terms
of univalent functions, Beltrami coefficients and quasisymmetric
homeomorphisms of the boundary of the unit disc.
May 1
Mitsuhiro Shishikura (Kyoto University
and Fields Institute)
Teichmuller contraction and renormalization
According to Royden-Gardiner theorem, any holomorphic
mapping between Teichmuller spaces does not expand the Teichmuller
distance. (Just like Schwarz-Pick theorem says that any holomorphic
mapping between hyperbolic Riemann surfaces does not expand the
Poincare metric.) In the theory of renormalizations, one often wants
to show that the renormalization map (which is defined in a transcendental
way) on the space of certain dynamical systems is hyperbolic or
contracting.
Therefore Royden-Gardiner theorem is an obvious
candidate of tools to obtain the contraction. This idea was first
used by Sullivan in his work on generalized Feigenbaum type renormalization.
In this talk, we will discuss two applications of Teichmuller
theory to renormalizations:
1. Parabolic renormalization for parabolic fixed
points and their perturbations. 2. Rigidity of real quadratic
polynomials only using Yoccoz's combinatorial a priori bounds.
For these cases, we deal with the Teichmuller
spaces of a disk or a punctured disk and show that a certain inclusion
map induces a contraction in Teichmuller distance.
Apr. 17
Jeremy Kahn (SUNY Stony Brook / Fields Institute)
The complex a priori bounds, continued
We describe how to reduce the a priori bounds for
bounded-primitive type renormalization to a simple combinatorial
statement regarding the combinatorial dynamics of arcs. We show
how the combinatorial statement follows from the expanding dynamics
on the Hubbard tree.
Apr. 10
Mary Rees (Liverpool)
A fundamental domain for V_{3}.
Abstract: We consider the space V_{n} of quadratic
rational maps with one named critical point of period n, quotiented
by M\"obius conjugacy preserving named critical points. Thus,
the space V_{1} is the space of all quadratic polynomials up to
affine conjugacy. The parameter space V_{1} must be one of the most
studied in all dynamics. But V_{1} differs from most other parameter
spaces in an important respect: there is a natural ``base map''
and, within the Mandelbrot set, natural paths, up to a natural homotopy,
to any other map in the Mandelbrot set. The simplest parameter space
for which this fails to be true is V_{3}.
One can say (truthfully) that there is no canonical
choice of fundamental domain for V_{3,m}, which is obtained from
V_{3} by removing a natural dynamically defined puncture set.
I shall exhibit a fundamental domain, using the dynamical planes
of three maps within V_{3} and a theory known as the ``Resident's
View''. This enables one to at least formulate an analogue of
MLC for this family.
Three parts of the fundamental domain are straightforward
(although the proof in one of these cases is probably new). The
structure of the fourth part is much more interesting, involving
a spiral in the dynamical plane of the so-called ``aeroplane''
quadratic polynomial z\mapsto z^{2}+c for the (unique) real parameter
c for which the critical point 0 has period 3.
Apr. 3
Matilde Martinez (Fields Institute)
Measures on hyperbolic surface laminations
We will consider laminations by hyperbolic Riemann
surfaces, and different
measures that can be associated with these objects (holonomy-invariant
measures, harmonic measures, measures invariant under the geodesic
and
horocycle flows). We will state some results that show how these
measures
are related. We will mainly focus on two families of examples: Riccati
foliations and Hilbert modular foliations.
Mar. 20
Peter Makienko
Remarks on Ruelle Operator, Invariant Differentials and invariant
line fields problem.
Abstract: TBA
Mar. 13th
**12PM (Note special time**)
Special Brown Bag Lunch Dynamical Systems
Seminar
Dierk Schleicher (IU Bremen), Johannes Rueckert (IU
Bremen), Magnus Aspenberg (Fields), and Vladim Timorin
(Stony Brook) + anyone who wants to can give input.
Combinatorics of Rational maps
Mar. 6
Roland Roeder (Fields)
Newton's Method in two complex variables: Indeterminant points
and the topology of basins of attraction
The equations x(x-1)=0, y^2+Bxy-y=0 are easy
to solve, but the Newton Map
N: C^2 \rightarrow C^2 for finding the four roots has very complicated
dynamics: N is four-to-one and N has points of indeterminacy.
Furthermore, high iterates of N have many points of indeterminacy.
By restricting to parameters |1-B|>1, all of these points of
indeterminacy are in the set X_l = Re(x) < 1/2, which is invariant
under N. If one wants to consider the homotopy type of a basin
of attraction, W(r_i), for one of the roots r_i \in X_l under
N, one encounters a kind of ``topological indeterminacy.'' When
studying the homotopy type of a loop \gamma in W(r_i), should
one consider the homotopies that hit the points of indeterminacy
of N^k or should one avoid them? Both seem reasonable. To avoid
such questions, one can perform blow-ups at the points of indeterminacy
of all iterates of N, obtaining a new space X_l^\infty from X_l
on which all iterates of N are defined.
We show how to make precise the notion of linking
numbers in X_l^\infty, overcoming a different kind of indeterminacy
that is a result of the fact that H_2(X_l^\infty) is infinitely
generated. Having developed this technology, I will explain how
we can use it to study the homotopy type of the basins of attraction
W(r_i) within X_l^\infty.
Feb. 27
Robert Devaney (Boston University)
Rings around the McMullen Domain
Feb. 13
Andrzej Bis (University of Illinois
at Chicago)
Dynamics of foliated spaces in codimension greater than one
Abstract. Dynamics of foliated spaces can be characterized
by the exceptional minimal sets and topological entropy. Dynamical
theory of codimension one foliations was developed by Hector, Cantwell
and Conlon, and others. We present some results on exceptional minimal
sets, which are analogous to the attractors in a standard dynamical
system, of foliated spaces in codimension greater than one.
Feb. 6
Yoel Feler (Fields Institute)
Holomorphic endomorphisms of configuration spaces
Abstract: The most traditional configuration space
C(X,n) of a complex space X consists of all n point subsets ("configurations")
Q in X.
If X carries an additional geometric structure, it may be taken
into account; say if X=CP^m or C^m, the space C(X,n;gp) of geometrically
generic configurations consists of all n point configurations Q
such that no hyperplane in X contains more than m points of Q. An
automorphism T of X (preserving an additional geometric structure,
whenever it is relevant) produces a holomorphic endomorphism f of
the configuration space via f(Q)=TQ. If the automorphism group Aut
X is a complex Lie group, one may take T=T(Q) depending analytically
on a configuration Q and define the corresponding holomorphic endomorphism
f by f(Q)=T(Q)Q. Such a map f is called tame. In the talk, we shall
see that for every non-hyperbolic Riemann surface X all "non-degenerate"
holomorphic endomorphisms of configuration spaces C(X,n) are tame.
To some extent, this is true also for spaces of geometrically generic
configurations.
Jan. 30
Tomoki Kawahira (Fields Institute)
Tessellation and Lyubich-Minsky laminations associated with quadratic
maps
Abstract: In 1990s, M.Lyubich and Y.Minsky introduced
the hyperbolic 3-laminations associated with rational maps as an
analogue of the hyperbolic 3-manifolds associated with Kleinian
groups. In this talk I will present a new method to describe topological
and combinatorial changes of laminations associated with hyperbolic-to-parabolic
degeneration of quadratic maps.
The method is based on tessellation of filled Julia sets, which
gives a nice organization of the dynamics inside the filled Julia
set like
external rays outside.
Jan. 23
Dierk Schleicher (International
University Bremen)
Dynamics of transcendental entire functions from the point of
view of polynomials
Abstract: In this talk, we will discuss some fundamentals
of iterated entire functions and indicate why and how they differ
from polynomial dynamics, with a special focus on the simplest representatives
in both cases, and a view towards generalization.
Jan. 16
Dmitrii V. Anosov (Steklov Mathematical
Institute)
A lemma about families of epsilon pseudo-trajectories revisited
In hyperbolic dynamics there are results related
to the existence of a true trajectory near an epsilon pseudo-trajectory
for sufficiently small epsilon (although, formally, some of these
results are expressed rather differently.) Many years ago I found
a lemma which covers most of these questions. The proof is rather
involved and some famous mathematicians expressed complaints about
the difficulty. In this talk, I will present a simplified version
of the proof.
Dec. 5
Viviane Baladi (Institut Mathematiques
de Jussieu)
Anisotropic spaces of distributions and dynamical zeta functions
Abstract: (Joint work with M. Tsujii) The Ruelle
transfer operator is a powerful tool in ergodic theory, which involves
composition with the dynamics. Many relevant dynamical systems are
hyperbolic, i.e. they involve contracting and expanding directions.
Composition with a contraction
improves regularity - but composing with an expanding map "worsens"
regularity: It has been an open problem for many years to find a
space
of distributions on which composition by a hyperbolic diffeomorphism
(of finite smoothness) can be well understood. Last year we constructed
such a space and estimated the essential spectral radius of the
transfer operator on this space. After recalling this result, we
shall describe more recent progress including spectral interpretation
of zeroes of dynamical determinants.
Nov. 28
Kristian Bjerklov (University
of Toronto)
The dynamics of the quasi-periodic Schroedinger cocycle at the
lowest energy of the spectrum
Abstract: We will study properties of the quasi-periodic
Schroedinger equation at the lowest energy of the spectrum. This
will lead us into the study of phase transitions. Moreover, we will
answer a question by M. Herman concerning the geometry of a certain
minimal set - a non-chaotic strange atractor - of the projective
Schroedinger cocycle. We study the case of large coupling constant
and Diophantine frequency.
Nov. 25, 1:10 p.m.
**Note: special day and time
Mitchell Feigenbaum (The Rockefeller
University)
Exponents in period doubling
Nov. 24, 1:10 p.m.
**Note: special day and time
Yulij Ilyashenko (Cornell University)
Topological properties of polynomial and analytic foliations
Abstract: Geometrical study of holomorphic foliations
of the complex plane, both projective and affine, lies on the boundary
of differential equations, topology and complex analysis. Foliations
of \Bbb CP^2 have an algebraic origin: they are defined by polynomial
vector fields, but their behavior is highly transcendental. Their
properties are drastically different from those of real polynomial
vector fields. Properties of density of leaves, absolute rigidity
and existence of a countable number of limit cycles were discovered
by different authors in 60s and 70s. The talk will present these
results together with a survey of the further development and open
problems.
Foliations of \Bbb C^2 have an analytic origin: they are defined
by analytic vector fields. Generic properties of these fields were
studied very recently. Yet genericity of density of leaves and existence
of the infinite number of complex limit cycles is recently proved.
Moreover, generic leaves of such foliations are either disks, or
cylinders. These results are obtained by graduate students Firsova,
Kutuzova and Volk.
Nov. 21
Konstantin Khanin (University of
Toronto)
Minimizers for random Lagrangian systems
Abstract: We shall discuss random Aubry-Mather theory
and prove that for time-dependent random Lagrangian systems on compact
manifolds there exists a unique global minimizer. In the one-dimensional
case we show that the global minimizer corresponds to a hyperbolic
invariant measure for the random Lagrangian flow. We also discuss
dynamical properties of shocks and show that their global structure
is quite rigid and reflects the topology of the configuration manifold.
Nov. 14
** talk at 4:10 p.m.
Israel Sigal (University of Toronto).
Spectral Renormalization Group and Theory of Radiation
Abstract: Non-relativistic quantum electrodynamics
describes interaction of charged particles (electrons and nuclei)
with quantized electro-magnetic field (photons). The key problem
here is to describe emission and absorption of radiation by systems
of matter such as atoms and molecules. In this talk I will present
some recent rigorous results on the problem of radiation and describe
a novel renormalization group technique used in proving these results.
I will not assume any prior knowledge of quantum field theory or
quantum mechanics.
Nov. 7
Marco Martens (University of Groeningen)
Henon renormalization (I)
Abstract: This mini-course will introduce a renormalization
operator for dissipative Henon-like maps. The fixed point of the
one-dimensional renormalization operator will also be a hyperbolic
fixed point of the Henon-renormalization operator. This corresponds
to universal geometrical properties of the Cantor attractor of infinitely
renormalizable Henon-like maps. However, the two-dimensional theory
is richer than the unimodal case. In particular, the Cantor attractor
is not rigid, does not lie on a smooth curve and generically does
not have bounded geometry. The quantitative aspects of these phenomena
are controlled by the average Jacobian.
The global topological properties of finitely renormalizable Henon-like
maps in phase and parameter space are also controlled by the average
Jacobian. In particular, density of hyperbolicity will be discussed
in a neighborhood of the infinitely renormalizable maps.
Oct. 31
Hans Koch (University of Texas,
Austin)
Renormalization of vector fields (I)
Abstract: This mini-course covers some of the recent
developments in the renormalization of flows - mainly Hamiltonian
flows and skew flows. After stating some of the problems and describing
alternative approaches, we focus on the definition and basic properties
of a single renormalization step. A second part deals with the construction
of conjugacies and invariant tori, including shearless tori, and
non-differentiable tori for critical Hamiltonians. Then we discuss
properties related to the spectrum of the linearized renormalization
transformation, such as the accumulation rates for sequences of
closed orbits. The last part describes extensions from "simple"
to Diophantine rotation vectors. This involves sequences of renormalization
transformations that are related to continued fractions expansions
in one and more dimensions. Whenever appropriate, the discussion
of details will be restricted to special cases where inessential
technical complications can be avoided.
Oct. 24
Michael Shub (U Toronto)
Lower bounds for the entropy in several families of dynamical
systems
Abstract: Using soft techniques we prove lower bounds
for the maximum entropy of a system in a family in terms of the
entropy of a random product of the systems in the family. We accomplish
this for two families of immersions of the circle. For one family
this is joint work with Leonel Robert and Enrique Pujals and the
other Rafael de la Llave and Carles Simo. Time permitting we recall
a two dimensional analog whose entropy properties are still unknown,
but for which partial
results have been achieved in joint work with Francois Ledrappier,
Carles Simo and Amie Wilkinson.
Oct. 17
Robert MacKay (University of Warwick, UK)
Some robustly mixing fluid flows
Abstract: I suggest an example of a C^3 divergence-free
vector field in a domain of R^3 with smooth boundary, vanishing
on the boundary, which is mixing and remains so for all small
perturbations in this class. Two other candidates are also presented.
Oct. 10
Thankgiving holiday
Oct. 3
Charles Pugh (UC Berkeley)
Smoothing Topological Manifolds
Abstract: The Cairns-Whitehead Smoothing Theorem
is proved by dynamical systems methods, namely the Invariant Section
Theorem.
Sept. 26
Roland Roeder (Fields Institute)
Super-stable manifolds for Newton's methods in two complex
variables
Abstract: While the equations x(x-1)=0, y^2+Bxy-y=0
are easy to solve, the dynamics of the Newton map N(x,y) for finding
the four roots is quite complicated. In particular, N is many-to-one
and N has points of indeterminacy.
The two vertical lines x=0 and x=1 are invariant under N and super-attracting.
Within these lines the ''circles'' Re(y) = 1/2 and Re(y) = (1-B)/2,
respectively, are hyperbolically repelling with multiplier 2.
In this talk we will prove that these circles have superstable
manifolds of real dimension 3 using the technique of holomorphic
motions. These manifolds extend to all points with Re(x) <
1/2 and Re(x) > 1/2 respectively and provide insight into the
topology of the basins of attraction for the four roots.
This work follows the ideas of John H. Hubbard and Sebastien Krief.
Sep. 19
M. Shishikura, Kyoto University
Renormalization for irrationally indifferent fixed points of
holomorphic maps
Abstract: Indifferent fixed points of holomorphic
maps give rise to delicate problems such as linearization problems,
discontinuous Julia sets etc. In this talk, we review the study
of those phenomena from the renormalization point of view. We
define a certain class of holomorphic maps with "non-degenerate"
parabolic fixed points. The parabolic renormalizaion is defined
for this class and shown to leave the class invariant. Then the
class is still invariant under a small perturbation, therefore
we can handle irrationally indifferent fixed points with large
continued fraction coefficients. This is a joint work with Hiroyuki
Inou.
We will compare this approach with Yoccoz's and McMullen's renormalizations.
We will also mention possible applications such as Buff-Cheritat's
work toward positive measure Julia


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Ethical Guidelines for Addiction Treatment Professionals
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Ethical Guidelines for Addiction Treatment Professionals
Feature Articles																		 -
Professional Ethics
Sunday, 31 March 2002 16:00
The ability to recognize and respond appropriately to ethical dilemmas encountered while treating addictive disorders is a complex task that cannot be taken for granted by even experienced counselors. Full caseloads and busy schedules provide few opportunities for in-depth examinations of ethical dilemmas that often demand an on-the-spot decision. This article sets forth a pragmatic set of principles that can help counselors to evaluate ethically challenging situations. While these ethical principles are relevant to almost any counseling situation, this article focuses on how they apply to the treatment of substance and behavioral addictions.
Numerous written codes of ethical conduct exist to guide the many different counseling professions. These documents may be more useful for giving clients and the public an assurance of the ethical parameters of professional behavior than in providing counselors with a useful frame of reference for dealing with day-to-day dilemmas. There is also an important difference between merely abiding by rules of conduct and embodying the ideals contained within them (Coale, 1998; Tjeltveit, 1999). A set of common principles derived from these various codes must be sufficiently broad enough to take into account the rich variety of practice settings, counseling theories and treatment approaches in which addiction counselors operate. Any less inclusive formula for determining whether a counselor's behavior is ethically appropriate requires knowledge of the context in which it occurs. For example, vigorously challenging a client's beliefs or behaviors may be ethically justifiable under one set of circumstances but not another (Tjeltveit, 1999). Similarly, different counselors may respond to an identical ethical dilemma in very distinct yet equally justifiable ways. What follows are six core ethical guidelines that are sufficiently broad and context-free to serve as a useful frame of reference in day-to-day counseling practice. These six guidelines are to provide informed consent; operate in a competent and theoretically sound manner; insure confidentiality of client information; maintain appropriate relationship boundaries; utilize adequate consultation; and to honor diverse personal and cultural values (Corey et al., 1998).
Informed consent
Informed consent is the fundamental bedrock of ethical practice, because it helps to solidify the client's autonomy in matters that affect the entire course and direction of counseling. Counselors may not always fully appreciate the lengths they must go to in order to ensure that important decisions about treatment issues are truly made from a basis of informed choice. Rather than being a one-time event, informed consent is an on-going collaborative effort between client and counselor for establishing and continuously monitoring the goals and strategies of counseling as well as the roles, rights, and responsibilities of all parties (Tjeltveit, 1999).
A client has a right to know which treatment modalities an addiction counselor typically recommends, such as group therapy, couples therapy, family therapy, medication, support group attendance, and so forth. Counselors often don't take the time to explicitly discuss the expected benefits and potential risks of their services, as well as any alternative treatment approaches that may be available to the client. Informed consent also includes information about the anticipated duration of treatment and any situations that could result in a counselor prematurely terminating services. In addition, clients should know the policy for resolving disputes as well as all pertinent financial aspects of the counseling relationship; counselors should also be open to discussing their background and theoretical orientation (Houston-Vega and Nuehring, 1997). Due to the large volume this information may constitute, the counselor may choose to convey it by a combination of verbal and written means.
A client's informed consent is not in itself sufficient to determine whether a counselor's behavior is ethical. It's conceivable that clients might be willing to give their approval to any number of ethically inappropriate behaviors, so a counselor needs other core principles to guide the ethical decision-making process.
Competence and established theory
A counselor has an ethical responsibility to practice only within the scope of his or her professional competence. Some typical indicators of competence include education, experience, training, and certification (Pope and Vasquez, 1998). Competence in one clinical area doesn't necessarily translate to another. Counselors with extensive experience treating general psychiatric disorders aren't necessarily competent to meet the specific needs of addicted clients, just as addiction counselors without advanced training don't always adequately recognize signs of psychiatric disorders. Cross-referral between such specialists is necessary in such situations.
One often-overlooked component of competency is a counselor's ability to clearly describe the theoretical basis for providing a particular clinical service. Just because a client's case turned out all right doesn't necessarily justify a counselor's actions if they otherwise lack adequate theoretical support. It is important to do the right thing for the right reason, not just for the right result. Counselors operating without the benefit of a clear theory are likely to rely too much on a combination of intuition, habit, consensus and personal preference (Herring, 2001; Tjeltveit, 1999; Corey et al., 1998). Clients deserve the knowledge and right to accept or reject treatment that represents a particular theoretical orientation. In the absence of information to the contrary, clients will assume that whatever form of counseling they are receiving is the only available or appropriate choice.
Confidentiality
Another core ethical principle is for a counselor to vigilantly guard against unauthorized disclosure of client information. The assurance of confidentiality is a fundamental guarantee, but it is not an absolute one. Several ethical dilemmas involving confidentiality commonly arise in the treatment of addictive disorders:
Duty to Warn/Protect. It is widely accepted that counselors have a general obligation to warn or protect people whom a client places in imminent harm. The right to confidential treatment is therefore balanced by the need to ensure the safety of others. The beginning of the counseling relationship is the most appropriate time for a client to learn about these limits of confidentiality as well as any safeguards necessary to protect others, such as policies on notifying law enforcement personnel if a habitual DUI offender drives to a counseling appointment while apparently intoxicated.
Clients who inject drugs or engage in sexually risky behavior while chemically impaired may expose others to the risk of HIV infection. Courts have not generally applied duty-to-warn standards to these situations (Houston-Vega and Nuehring, 1997). Balancing the counselor-client relationship with the protection of at-risk populations is a very complex and emotionally charged situation.
Counselors should inform clients about their policy for dealing with HIV-related confidentiality issues, educate clients about the health risks of their specific sex and drug practices, communicate any concerns that arise during the course of treatment, offer to help communicate information to partners, and consult with colleagues as deemed appropriate.
Minors and Families. All states require counselors to report situations in which minors are in danger of harm, although specific state statutes differ (Corey et al., 1998). As most counselors know, it can be difficult to distinguish potential from probable risk. For instance, a client who admits to blackouts may deny that she places her children in any danger. A counselor who decides not to notify the designated reporting agency in such a situation should document the basis for this decision in the clinical record. Consultation in these situations is again extremely valuable in helping a counselor maintain much-needed clinical objectivity.
Counselors who treat minors for substance use disorders need to clearly establish the extent to which parents have the right to information that is disclosed by their children. A minor may be reluctant to talk honestly if confidentiality boundaries are not clear, and the therapeutic alliance may be crippled if a counselor who is unclear on the limits of confidentiality later provides information to parents. Counselors should be familiar with federal law on confidentiality of alcohol and drug abuse records for minor clients (Confidentiality of Alcohol and Drug Abuse Patient Records, 1998) as well as any applicable state laws, and should seek professional consultation whenever questions arise.
A major ethical concern that arises when counseling couples or families is how to deal with the emergence of secrets that so often accompany addictive disorders. For example, consider the situation that could arise when providing marital counseling to a couple if a husband who attends a session by himself announces that he's relapsed on cocaine but is unwilling to admit this to his wife. A counselor who keeps this information secret is not fostering a climate of honesty. On the other hand, revealing information that a client reasonably presumed would remain confidential will damage that client's trust, while threatening to summarily end treatment if the client isn't honest with his spouse is a form of coercion and potential abandonment. This again points to the necessity of informed consent: whatever approach a counselor takes in response to these types of situations needs to be thoroughly discussed at the beginning of the counseling relationship so that all clients are aware of the consequences of disclosure (Corey et al., 1998; Herring, 2001).
Maintaining appropriate boundaries
The next core concept of ethical counseling involves the complex area of maintaining appropriate professional boundaries. Most counselors know that there are ethical risks to developing relationships outside of the therapeutic role, such as counseling a friend or pursuing business or social interactions with clients. These types of dual relationships can impair a counselor's objectivity or unintentionally exploit a client's dependence (Pope and Vasquez, 1998). Yet some subtle boundary issues present ethical dilemmas that are neither obvious nor easily avoidable.
Counselor self-disclosure. In order to maintain appropriate clarity of roles, a counselor should only reveal intimate personal information when doing so is clearly relevant to the client's treatment goals, carefully tailoring this information to the client and paying close attention to how such sharing affects the clinical relationship (Bloomgarden, 2000). Consultation with colleagues and supervisors can help insure that the true purpose for disclosing personal information is to meet the emotional needs of the client rather than the counselor. One helpful guideline is for a counselor to reveal information about a personal life problem only well after it has been resolved, and not while it is an ongoing issue (Hunter and Struve, 1998).
Touch. Since a significant proportion of clients with addictive disorders have a history of childhood trauma (Briere, 1992), even a simple act of touch can convey a variety of ethically ambiguous messages. The history of addiction support is replete with reassuring hugs. It's very important for a counselor who engages in any form of physical contact with clients to have a highly developed sense of boundaries and an astute awareness of the clinical implications of this behavior. The initial stages of the therapeutic relationship may not provide sufficient emotional safety to ensure that a client can discuss any uncomfortable feelings involving the counselor's touch (Hunter and Struve, 1998).
Sexual attraction. Sexual involvement with a client constitutes a profound ethical violation with severe emotional consequences. However, occasional sexual feelings are not in themselves either unethical or even particularly abnormal in the context of an intimate therapeutic relationship (Pope and Vasquez, 1998). Counselors must acknowledge and appropriately process the existence of these feelings when they emerge in order to successfully understand and redirect them. The presence of intense preoccupation or sexual fantasies involving clients needs to be forthrightly discussed in consultation and supervision.
Recovery Boundaries. Counselors who have successfully dealt with addictive disorders in their own lives can often relate to their clients with profound understanding, empathy, and clarity. However, they may also be overly devoted to the treatment approach they personally found successful (Johnson, 2000). For instance, counselors who are strongly 12-step oriented may discount non-abstinence models for addressing substance abuse, such as risk reduction strategies, which threatens to place clients into a one-size-fits-all philosophy of care.
A counselor who is candid about being "in recovery" may give clients hope and reduce the shame that inevitably accompanies addiction. However, too much disclosure can be intrusive and distracting for some clients, and can even inadvertently generate unrealistic expectations or a sense of inadequacy (Bloomgarden, 2000). Counselors should therefore carefully reveal information about their personal addiction experience only in as much detail as is necessary to meet a compelling and clearly defined clinical need.
A counselor who is treating clients with substance use disorders should not be unsuccessfully fighting the same battle. Sustained abstinence from addictive behavior is an inescapable ethical responsibility for anybody working in this field. Counselors with less than several years of recovery time may easily lose objectivity when dealing with clients whose clinical picture mirrors their own personal experience. Heightened levels of consultation and supervision are highly advisable in such circumstances.
Nobody is immune to relapse, regardless of the length of time in recovery. A counselor who reverts to a previous pattern of addictive behavior must face the ethical dilemma of whether to limit, suspend, or terminate clinical duties. Abruptly withdrawing services from a client due to this (or any other) form of counselor impairment is likely to be deeply disruptive to the client's healing process (Bissell and Royce, 1994). Clients in such situations must be given the opportunity to continue counseling with another provider. There is no one answer to the problem of counselor relapse that is completely satisfying. In this regard the difference between a temporary "slip" that can result in increased self-awareness and an unrestrained relapse may be useful in determining a counselor's overall level of clinical impairment. These decisions should be made in a process of supervision and consultation so that the counselor is not relying on his or her personal judgment, which may be impaired.
All counselors who are in recovery from addictive behavior must establish whatever safeguards are necessary to ensure the maintenance of a personal program of sobriety. This may include establishing boundaries around support group meetings that clients are asked not to attend. It is not ethically appropriate for counselors in 12-step recovery to sponsor their own patients or chair meetings where they are employed (Bissell and Royce, 1994).
Supervision
The next core ethical concept is for counselors to have a structured process for discussing formulations, interventions, reactions, and inevitable difficulties with supervisors and colleagues. There is a heightened need for supervision and consultation for counselors who are working on the outer limits of either personal competence or established theory (Corey et al., 1998). For example, a counselor attempting to implement a new technique should utilize close supervision until it becomes fully integrated into his or her set of skills.
It's an unfortunate reality that not all clinical supervisors have adequate experience or knowledge in the treatment of addictive disorders. In such cases a counselor needs to seek out additional sources for case consultation.
One solution is to set up and utilize informal telephone and e-mail networks which can be established fairly easily with colleagues and contacts made through professional affiliations. When consultation is not available for discussing a clinical or ethical dilemma, a counselor should document in the clinical record a summary of the relevant issues as well as any action taken in response to it.
Honoring diverse values
All of the preceding ethical principles involve some specific actions for a counselor to take. However, the ethical dimension of counseling goes far beyond merely abiding by a procedural checklist. An ethical counselor consistently demonstrates respect for the client as a person by honoring diversity and appreciating the degree to which his or her personal values influence the entire process of counseling. Since counselors are in the business of helping clients change some aspect of their lives, the great ethical challenge is to effectively guide the process and direction of this change without undermining the client's autonomy. This ethical use of a counselor's influence is a skill that cannot be taught as much as developed.
Since every person's view of the world represents a unique combination of diverse personal and cultural perspectives, it is inevitable that counselors will sometimes hold views that are very different from their clients. No counselor is ethically justified in assuming that the way he or she views life is the way everybody else does, is the right way, or is the only way. However, some counselors act as if the way to avoid imposing their personal values is to simply not talk about them.
But biases don't lose their influence just because they're not discussed; in fact they often become less amenable to change. It is often more ethically beneficial for a counselor to invite discussion about his or her personal values while conveying an ability to respect and work with many alternative positions. A counselor doesn't need to be neutral about his or her values in order to be nonjudgmental (Coale, 1998; Tjeltveit, 1999).
When a client and a counselor hold fundamentally incompatible value orientations, the counselor should either refer the case or strive to help the client achieve the goals of counseling within the context of the client's value system rather than attempting to change those values. If a counselor finds it necessary to attempt to modify a client's values, this should be done to no more extent than is necessary to address that client's particular focus of treatment.
Counselors often avoid initiating discussion with clients about the ethical dimensions of clinical issues. Sometimes this reluctance stems from the fear of appearing moralistic, but it also reflects a general tendency of the counseling profession to be ethically inarticulate. It takes considerable effort and skill to engage in thoughtful dialogue about the ethical aspects of life, but doing so can have great benefit for clients whose history of addiction is marked by diminished personal integrity. While this does not guarantee a positive clinical outcome, it does foster the kind of therapeutic environment for a client to utilize the counseling experience to its fullest potential.
These guidelines are not an exhaustive review of every ethical issue related to addictions counseling and they cannot substitute for a counselor's knowledge of his or her professional code of conduct. Many clinical situations require a more detailed examination of the ethical issues involved or compliance with specific codified procedures, such as guidelines for research involving human subjects. Although counselors almost always operate within ethical parameters, these principles can serve as a helpful reminder of some of the important points to consider when evaluating the proper ethical stance to take when dealing with the many complexities of addictions counseling.
Bill Herring, LCSW, is a privately practicing clinician in Atlanta. He is a member of the board of directors of the National Council on Sexual Addiction and Compulsivity. He can be reached via e-mail at
This e-mail address is being protected from spambots. You need JavaScript enabled to view it
References
Bissell, L. and Royce, J. (1994). Ethics for Addiction Professionals. Center City, MN: Hazelden.
Bloomgarden, A. (2000). Self-disclosure: is it worth the risk? The Renfrew Center Foundation Perspective, 5 (2), 8-9.
Briere J. (1992). Child abuse trauma: Theory and treatment of the lasting effects. Newbury Park, CA: Sage.
Coale, H. (1998). The Vulnerable Therapist: Practicing Psychotherapy in an Age of Anxiety. New York: Haworth.
Confidentiality of Alcohol and Drug Abuse Patient Records, 42 CFR 2.14 (1998)
Corey, G., Corey, M. and Callanan, P. (1998). Issues and Ethics in the Helping Professions. Pacific Grove, CA: Brooks/Cole.
Herring, B. (2001). Ethical guidelines in the treatment of compulsive sexual behavior. Sexual Addiction & Compulsivity: The Journal of Treatment and Prevention, 8, 13 - 22.
Houston-Vega, M. and Nuehring, E. (1997). Prudent Practice: A Guide for Managing Malpractice Risk. Washington, DC: National Association of Social Workers Press.
Hunter, M. and Struve, J. (1998). The Ethical Use of Touch in Psychotherapy. New York: Sage.
Johnson, C. (2000). Been there, done that: the use of clinicians with personal recovery in the treatment of eating disorders. The Renfrew Center Foundation Perspective, 5 (2), 1-4.
Pope, K. and Vasquez, M. (1998). Ethics in Psychotherapy and Counseling: A Practical Guide. San Francisco: Jossey-Bass.
Tjeltveit, A. (1999). Ethics and Values In Psychotherapy. New York: Routledge.
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Cathy Duncan
|69.138.75.xxx
|2012-02-26 16:52:28
At times hugs especially where there is female counselor and male client mayneed to ve discussed immedialtley in order to maintain the therapeutic.
Not allclients need that " reasurring" hug
Reply
0 0
Cathy Duncan
- Ethical Guideline for Addiction Treatment professi
|69.138.75.xxx
|2012-02-25 16:44:47
employed as a juvenile addictions counselor this article reiterates to me thatEthical guidelines for Addiction Counselors must be excuted in order to maximizethe success of all clients.
Developing a counselor client relationship withjuveniles can be challenging and rewarding. However the one delima thatsurpasses all others working with juvenile is confidentiality. Even though theysign consent forms for releaselof certain information it is very important to besure they understand what information they are consenting or authorizing to bereleased.
Their misunderstanding can damage the counselor client relationship
Reply
0 0
Ackson mwimbi
- This is an important aspect of the course
|69.171.160.xxx
|2012-02-25 04:29:03
I dont think anyone should be allowed to practice or work in an addiction fieldwithout taking this course.
Reply
0 0
Mayra Schneider
- student
|160.253.128.xxx
|2012-02-24 06:00:06
I thought it was very important what this article mentioned. That is, that
nomatter how much time the client have been sober he or she can alwaysrelapse.
Also, especially when we deal with addictions because of the stigmais always important to keep confidentiality. And of course, before I startworking with the client, the client must sign a consent.
Reply
0 0
Cathy Duncan
|69.138.75.xxx
|2012-02-25 17:11:54
Also remember counselors can also relapse.
When this happens that counselorwill need to work on their own soberity. In doing so that caseload-clients maynot receive the support they need from that counselor and shouls thatinformation be disclosed to a supervisor or kept confidential, what about theclient
Reply
0 0
Gwendolyn Jones
|198.200.181.xxx
|2011-02-23 05:44:43
I'm glad that the ethical guidelines have focus on tough.
While attending AA/NAmeetings, I always though that the "hug" thing was sometimes toopersonal. I'm glad that there are "rules" because some people areoffended and to gain good rapport from the very geginning I feel that"space" shows respect for both consumer and counselor.
In addition, theduty to warn/protect is a very tricky guideline in any situation.
As a goodcounselor you just have to face the fact that this guideline will benefiteveryone involved.
For example, if a client has revealed to you that he/sheuses hyperdemic needle that belong to a family member who has diabetes, to stopa possible infection of diseases, this should be reported to authorities.
Reply
0 0
Gwendolyn Jones
- Comments
|198.200.181.xxx
|2011-02-21 08:35:56
Although I had a general idea of ethics for addiction treatment professionals, Ifound the article very informative.
It answered many questions that I hadconcerning "what if" situations.
In addition, the article was writtenwhereas I clearly understood the gidelines.
Reply
0 0
Jessica James
|67.61.24.xxx
|2010-09-25 15:53:07
I found this article very helpful. I too did not realize until this article thatcouples in counseling had to sign confidentiality waivers.
Reply
0 0
shari k. ketterling
|68.92.113.xxx
|2010-06-12 17:44:01
Excellent information. I'm in my Master's in Psychology.
All of theabove information I have covered in my classes.
Confidentiality is extremelyimportant and the codes of ethics is a must.
Thank You
Reply
0 0
Regina Barbour
|173.124.138.xxx
|2010-01-10 16:22:18
I found the article to be very informative and needful.
I was very surprised tolearn that if a couple is in marital counseling that they have to sign aninformed consent in order to share what was shared in their individual session.
Reply
0 0
alfred francois
|71.191.171.xxx
|2008-01-04 12:43:16
i found this article very informative
Reply
0 0
walterene garrison
|72.219.201.xxx
|2007-10-07 11:01:39
I was impressed about the way confidentially is secured by state and federallaws.
I was surprised to learn that when a counselor is counseling to a marriedcouple, that if one is having a one on one with the counselor he must haveinformed consent to reveal what was discussed in the session with the otherfamily member.
I was slso surprised to see that a counselor can disclosure hispersonal information with the client as long as it is well after it has beenresolved.
I was also surprised to learn that if a counselor has sexual feelingsthat might jeopardize the counseling with the client that he has to go intoconsultation with a supervisor and reveal this.
Reply
1 0
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Math - Courses
You are in the official 1997-98 General Catalog
for California State University, Fresno.
Department of Mathematics
COURSES
Undergraduate Mathematics (Math) Courses
Graduate Mathematics (Math) Courses
Mathematics (Math)
ILR. ELM Basic Mathematics Skills (3-6; max total 6)
Prepares students for the ELM exam and for Math 4. The course takes two
semesters and reviews arithmetic, elementary algebra, and geometry. Note:
Enrollment is limited to freshmen who score lower than 370 on the ELM exam.
CR/NC grading only; not applicable toward baccalaureate degree
requirements.
AR. ELM Basic Mathematics Skills (3)
Develops problem solving skills in arithmetic (integers and rational numbers),
elementary algebra (exponents, roots, polynomials and rational expressions,
linear and quadratic equations, and graphing), and geometry (perimeters,
areas, volumes, triangle properties, parallelism, and perpendicularity).
CR/NC grading only; not applicable toward baccalaureate degree
requirements.
ARL. Elementary Algebra Laboratory (1)
Prerequisites: concurrently enrolled in Math AR and assigned to laboratory
after taking placement examination. Laboratory does not count toward baccalaureate
degree. Extra review and practice with skills essential to success in elementary
algebra. CR/NC grading only; not applicable toward baccalaureate
degree requirements.
4R. Intermediate Algebra (3)
Prerequisites: elementary algebra and geometry. Radicals, rational exponents,
quadratic equations, simultaneous linear equations, graphing inequalities,
complex numbers in rectangular form, introduction to exponential and logarithmic
functions, applications. CR/NC grading only; not applicable
toward baccalaureate degree requirements. (See Duplication
of Courses.)
4RL. Intermediate Algebra Laboratory (1)
Prerequisites: concurrently enrolled in Math 4R and assigned to laboratory
after taking placement examination. Laboratory does not count toward baccalaureate
degree. Extra review and practice with skills essential to success in intermediate
algebra. CR/NC grading only; not applicable toward baccalaureate
degree requirements.
5. Trigonometry (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught
intermediate algebra course. Concept of a function, sine and cosine functions,
tables and graphs, other trigonometric functions, identities and equations.
Trigonometric functions of angles, solution of triangles. (See Duplication
of Courses.) (CAN MATH 8)
6. Precalculus (4)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught
intermediate algebra course. Basic algebraic properties of real numbers;
linear and quadratic equations and inequalities; functions and graphs; polynomials;
exponential and logarithmic functions; analytic trigonometry and functions;
conics; sequences, and series. (CAN MATH 16)
11. Elementary Statistics (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught
intermediate algebra course. Illustration of statistical concepts: elementary
probability models, sampling, descriptive measures, confidence intervals,
testing hypotheses, chi-square, nonparametric methods, regression. It is
recommended that students with credit in Math 72 or 75 take Math 101. General
Education CORE, Quantitative Reasoning. (CAN STAT 2)
14. Introduction to Discrete Mathematics (3)
No credit if taken after Math 75. Prerequisite: Students must take the ELM
exam; students who do not pass the exam must record a grade of C
or better in a college-taught intermediate algebra course. Set theory, relations
and functions, logic, proof techniques, number systems.
41. Number Systems (3)
Not open to mathematics majors. Prerequisite: Students must take the ELM
exam; students who do not pass the exam must record a grade of C
or better in a college-taught intermediate algebra course. Designed for
elementary credential candidates. Development of rational number system
and its subsystems from the informal point of view; sets, relations and
operations, equivalence classes; definitions of number systems and operations;
algorithms for operations; prime numbers, divisibility tests; ratios. (CAN
MATH 4)
43. Elementary Problem Solving (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught
intermediate algebra course. The purpose of this course is to develop problem-solving
skills using elementary mathematics.
45. What is Mathematics? (3)
Prerequisite: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught
intermediate algebra course. Intended primarily for liberal arts students.
Topics: mathematics and social science, mathematics of shape and growth,
statistics, mathematics of management science and mathematics of computers.
General Education CORE, Quantitative Reasoning.
61. Geometry and the Imagination (3)
Prerequisites: Students must take the ELM exam; students who do not pass
the exam must record a grade of C or better in a college-taught
intermediate algebra course. Topics in Geometry. May include, but is not
restricted to, tilings and tessellations, regular polyhedra in 3 and 4 dimensions,
ruler and compass constructions, map coloring.
70. Mathematical Analysis for Life Sciences (4)
No credit if taken after Math 72 or 75; one unit of credit if taken after
Math 71. Prerequisite: Students must take the ELM exam; students who do
not pass the exam must record a grade of C or better in a
college-taught intermediate algebra course. Functions and graphs, limits,
derivatives, antiderivatives, differential equations, and partial derivatives
with applications in the Life Sciences. General Education CORE, Quantitative
Reasoning.
71. Elementary Mathematical Analysis I (3)
No credit if taken after Math 70, 72, or 75. Prerequisite: Students must
take the ELM exam; students who do not pass the exam must record a grade
of C or better in a college-taught intermediate algebra course.
Review of algebra, real numbers, inequalities, function, graph, finite induction,
limit, differentiation of algebraic functions and applications to extrema,
mean value theorem, l'Hôpital's rule.
72. Elementary Mathematical Analysis II (3)
No credit if taken after Math 75; 2 units of credit if taken after Math
70. Prerequi sites: Math 71 and trigonometry. Analytic geometry and calculus
of polynomials, rational functions, transcendental functions; polar coordinates,
conic sections, integration and applications. General Education CORE, Quantitative
Reasoning.
75. Mathematical Analysis I (4)
Two units of credit if taken after Math 70; 3 units of credit if taken after
Math 71; 2 units of credit if taken after Math 72. Prerequisite: elementary
geometry, intermediate algebra, trigonometry, or Math 6. In addition, students
must take the ELM exam; students who do not pass the exam must record a
grade of C or better in a college-taught intermediate algebra
course. Inequalities, functions, graphs, limits, continuity, derivatives,
antiderivatives, the definite integral, and applications. General Education
CORE, Quantitative Reasoning. (CAN MATH 18)
76. Mathematical Analysis II (4)
Prerequisite: Math 75. Transcendental functions, techniques of integration,
improper integrals, conic sections, polar coordinates, infinite series.
(CAN MATH 20)
77. Mathematical Analysis III (4)
Prerequisite: Math 76. Vectors, three dimensional calculus, partial derivatives,
multiple integrals, Green's Theorem, Stokes' Theorem. Use of the microcomputer
as an exploratory tool in the calculus. (3 lecture, 2 lab hours) (Computer
lab fee, $15) (CAN MATH 22)
81. Applied Analysis (4)
Prerequisite: Math 77. Introduction to ordinary linear differential equations;
solutions by power series and Laplace transforms. Solution of systems of
equations. Introduction to Fourier series. Use of the microcomputer as an
exploratory tool. (3 lecture, 2 lab hours) (Computer lab fee, $15)
90. Directed Study (1-3; max total 3)
Independently arranged course of study in some limited area of mathematics
either to remove a deficiency or to investigate a topic in more depth. (1-3
hours, to be arranged)
101. Statistical Methods (4)
Prerequisite: Math 70, 71, or equivalent; no credit if taken after Math
108. Application of statistical procedures to examples from biology, engineering,
and social science; one- and two-sample normal theory methods; chi-square,
analysis of variance, and regression; nonparametric methods. Computerized
statistical packages are used.
107. Introduction to Probability and Statistics (3)
Prerequisite: Math 77 or concurrently. Basic concepts required for applications
of probability theory; standard discrete and continuous models; random variables;
conditional distributions; limit theorems.
108. Statistics (3)
Prerequisite: Math 107. Criteria used for selecting particular procedures
of data analysis; derivation of commonly used procedures; topics from sampling,
normal theory, nonparametrics, elementary decision theory.
109. Applied Probability (3)
Prerequisite: Math 107. Introduction to stochastic processes and their applications
in science and industry. Markov chains, queues, stationary time series.
110. Symbolic Logic (3)
(Similar to Phil 145; consult department.) Prerequisite: Math 75. An informal
treatment of the theory of logical inference, statement calculus, truth-tables,
predicate calculus, interpretations applications.
114. Discrete Structures (3)
Prerequisite: Math 76. Counting techniques, matrix algebra, graphs, trees
and networks, recurrence relations and generating functions, applied modern
algebra.
116. Theory of Numbers (4)
Prerequisite: Math 75. Divisibility theory in the integers, primes and their
distribution, congruence theory, Diophantine equations, number theoretic
functions, primitive roots, indices, the quadratic reciprocity law.
118. Graph Theory (3)
Prerequisite: Math 77. Trees, connectivity, Euler and Hamilton paths, matchings,
chromatic problems, planar graphs, independence, directed graphs, networks.
121. Numerical Analysis I (3)
Prerequisites: Math 77 and working knowledge of C, FORTRAN, or Pascal. Zeros
of nonlinear equations, interpolation, quadrature, systems of equations,
numerical ordinary differential equations, and eigenvalues. Use of numerical
software libraries.
121L. Numerical Analysis Laboratory (1)
Corequisite: Math 121. Optional computer laboratory for Numerical Analysis
I. Use of microcomputers to implement numerical algorithms. (2 lab hours)
(Computer lab fee, $15)
122. Numerical Analysis II (4)
Prerequisite: Math 121. Advanced topics from numerical linear algebra, function
approximation, fast Fourier transforms, and numerical partial differential
equations. Use of numerical software libraries. (3 lecture, 2 lab hours)
123. Topics in Applied Mathematics (3)
Prerequisite: Math 77. Vector spaces and linear transformations, eigenvalues
and eigen functions. Special types of linear and nonlinear differential
equations; solution by series. Fourier transforms. Special functions, including
gamma, hypergeometric, Legendre, Bessel, Laguerre, and Hermite functions.
Introduction to partial differential equations.
124. Applied Matrix Analysis (3)
Prerequisite: Math 77. Matrix algebra, systems of equations, eigenvalues,
eigenvectors, diagonalizations, functions of matrices with applications
to differential equations, optimization, and Markov chains.
128. Applied Complex Analysis (3)
Prerequisite: Math 77. Analytic functions of a complex variable, contour
integration, series, singularities of analytic functions, the residue theorems,
conformal mappings; emphasis on engineering and physics applications.
131. Game Theory and Linear Programming (3)
Prerequisites: Math 76. Introduction to linear programming, problem formulation,
adaptation of the Dantzig simplex algorithm to linear programming problems,
duality theory, transportation problems. Games of chance, strategy, minimax
theorem for two-person zero-sum games, relationship to linear programming.
143. History of Mathematics (4)
Prerequisite: Math 72 or 75. History of the development of mathematical
concepts in algebra, geometry, number theory, analytical geometry, and calculus
from ancient times through modern times. Theorems with historical significance
will be studied as they relate to the development of modern mathematics.
145. Problem Solving (3)
Prerequisite: Math 76. A study of formulation of problems into mathematical
form; analysis of methods of attack such as specialization, generalization,
analogy, induction, recursion, etc. applied to a variety of non-routine
problems. Topics will be handled through student presentation.
151. Principles of Algebra (4)
Prerequisite: Math 76. Equivalence relations; groups, cyclic groups, normal
subgroups, and factor groups; rings, ideals, and factor rings; integral
domains and polynomial rings; fields and field extensions.
152. Linear Algebra (4)
Prerequisite: Math 151. Vector spaces, linear transformations, matrices,
determinants, eigenvalues and eigenvectors, linear functions, inner-product
spaces, bilinear forms, quadratic forms, orthogonal and unitary transformations,
selected applications.
161. Principles of Geometry (3)
Prerequisite: Math 77. The classical elliptic, parabolic, and hyperbolic
geometries developed on a framework of incidence, order and separation,
congruence; coordinatization. Theory of parallels for parabolic and hyperbolic
geometries. Selected topics of modern Euclidean geometry.
165. Differential Geometry (3)
Prerequisite: Math 77. Study of geometry in Euclidean space by means of
calculus, including theory of curves and surfaces, curvature, theory of
surfaces, and intrinsic geometry on a surface.
171. Intermediate Mathematical Analysis I (4)
Prerequisite: Math 77. Sets, real numbers as a complete ordered field, its
usual topology, functions of a real variable, limits, continuity, uniform
continuity, differentiability, generalized mean value theorem, Riemann integrals,
series of functions, uniform convergence, and Fourier series of integrable
functions. (Formerly Math 171A)
172. Intermediate Mathematical Analysis II (4)
Prerequisite: Math 171. Differentiation of functions of several variables,
applications of partial differentiation, functions of bounded variation,
rectifiable curves, theory of Riemann-Stieltjes integration, multiple integrals
and line integrals, improper Riemann-Stieltjes integrals. Inverse and implicit
function theorems.
181. Differential Equations (3)
Prerequisite: Math 81 or 123. Definition and classification of differential
equations; general, particular, and singular solutions; existence theorems;
theory and technique of solving certain differential equations: phase plane
analysis, elementary stability theory; applications.
182. Partial Differential Equations (3)
Prerequisites: Math 81 or 123, and 171. Classical methods for solving partial
differential equations including separation of variables, Green's functions,
the Riemann-Volterra method and Cauchy's problem for elliptic, parabolic,
and hyperbolic equations; applications to theoretical physics.
190. Independent Study (1-3; max total 6)
See Academic Placement -- Independent
Study. Approved for SP grading.
191T. Proseminar (1-3; max total 9)
Prerequisite: permission of instructor. Presentation of advanced topics
in mathematics in the field of the student's interest.
198. Senior Project (3)
Prerequisites: senior standing or permission of instructor; Math 151, 171,
and 152. Independent investigation and presentation of an advanced topic
in mathematics. Satisfies the senior major requirement for the BA in Mathematics.
GRADUATE COURSES
(See Course Numbering System.)
Mathematics (Math)
202. Fundamental Concepts of Mathematics (3)
Prerequisites: Math 151, 161 and 171. Fundamental notions regarding number
theory, number systems, algebra of number fields; functions.
210. Foundations of Mathematics (3)
Prerequisite: Math 110 or 151. Formal introduction to theories of inference,
first order theories, completeness metatheorems, consistency metatheorems,
decision problems.
216. Topics in Number Theory (3; max total 6)
Prerequisite: Math 116. An investigation of topics having either historical
or current research interest in the field of number theory.
221. Advanced Numerical Analysis (3)
Prerequisite: Math 121. Linear equations and matrices; parabolic, hyperbolic,
and elliptic differential equations; constructive function theory.
223. Principles and Techniques of Applied Mathematics (3)
Prerequisite: Math 123. Linear spaces and spectral theory of operators.
224. Optimization Methods (3)
Prerequisite: Math 123. Techniques for optimizing static and dynamic systems,
calculus of variations, Hamiltonian canonical form, maximum principle, with
applications.
228. Functions of a Complex Variable (3)
Prerequisite: Math 128. Representation theorems of Weierstrass and Mittag-Leffler,
normal families, conformal mapping and Riemann mapping theorem, analytic
continuation, Dirichlet problem.
251. Abstract Algebra I (3)
Prerequisite: undergraduate abstract algebra. Groups, rings, integral domains,
and fields.
252. Abstract Algebra II (3)
Prerequisite: Math 251. Rings and ideals, modules, linear and multilinear
algebras, representations.
263. Point Set Topology (3)}
Prerequisite: Math 172. Basic concepts of point set topology, set theory,
topological spaces, continuous functions; connectivity, compactness and
separation properties of spaces. Topics selected from function spaces, metrization,
dimension theory.
265. Differential Geometry (3)
Prerequisites: Math 165, 172. Study of geometry of curves and surfaces in
Euclidean space; including an introduction to Riemannian geometry and theory
of manifolds.
271. Real Variables (3)
Prerequisite: Math 172. Theory of sets; cardinals; ordinals; function spaces,
linear spaces; measure theory; modern theory of integration and differentiation.
272. Functional Analysis (3)
Prerequisite: Math 271. The Lebesgue-Stieltjes integral and its generalizations,
integral equations, Hilbert and Banach spaces, linear transformations (bounded
and unbounded).
290. Independent Study (1-3; max total 6)
See Academic Placement -- Independent
Study. Approved for SP grading.
291. Seminar (3)
Prerequisite: graduate standing. Presentation of current mathematical research
in field of student's interest.
298. Research Project in Mathematics (3)
Prerequisite: graduate standing. Independent investigation of advanced character
as the culminating requirement for the master's degree. Approved for SP


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Harbhajan's case: Bhajji is all set to play again!
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mandira srivastavaJan 30 2008
Bhajji’s fans will be very delighted to see him playing on the ground again. Few hours before, Indian Cricket team that was ready to come back leaving the Australian tour in the mid, is all set to play for 20-20 match in Melbourne .
We might witness a healthy tough competition between the two leading teams of the world. Thank God!
The racism charges against Harbhajan Singh had been dropped but he has to pay 50 per cent of match fees. Don’t you think, this outcome was bound to happen and there was no other outcome possible? Ultimately,money rules over everything else. There is too much money at stake to cancel the tour both officially and unofficially A lot of money of the organizers, advertisers and sponsors could be saved due the decision of Indian team to play the one day series too.
We all know cricket is not only game but also a nice opportunity for corporate houses to advertise their products and services.nnterDefinitely, few people like me would not like to accept this judgment, it was Symonds who provoked Bhajji first then he should be the first one who should be punished (He should also give 50 percent of his match fee)! They are saying Bhajji is let off for his past good behavior, as if they are doing a favour to him and India.
Also the Australian team has proved the world that they are bunch of liars and cheats supported by Procter.No can one forget that India had defeated Australia in 20-20 match finals. Yes! We all Indian cricket enthusiastic are waiting for that magic again. Good luck,team India!via
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ChronicleLive - Lifestyle - Holiday Hypermarket - Foreign trips fall as durations rise
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Holiday Hypermarket
Foreign trips fall as durations rise
Jul 23 2010
By Holiday Hypermarket
Past summers have seen British holidaymakers frantically searching for foreign beach holiday deals year after year.
This overseas holiday trend has been growing at an average rate of 4% per year over the past 25 years, with tourists heading to the UK from overseas growing at an average of 3.2%.
The Office for National Statistics (ONS) reported that this trend changed in 2009, with 58.6 million UK holidaymakers heading overseas, a 15% drop on 2008. Overseas residents heading to the UK on holiday also fell from 31.9 million in 2008 to 29.9 million in 2009, a slower drop of 6.3%.
Surprisingly this drop is not exclusive to holidaymakers cutting back on their beach holiday deals abroad. In fact business visits were the hardest hit, falling by 23% among UK residents travelling abroad on business, compared to 19% of overseas business travellers heading here to the UK.
Holiday visits to relatives abroad by UK residents fell at a lower rate of 6.5% and to friends abroad at a higher 15%. The number of overseas residents visiting the UK to see friends and family also dropped by 9.7%.
ONS reported that it is not all doom and gloom for some sectors of the UK though, as expenditure of overseas visitors during their UK holidays grew from £16.3 billion in 2008 to £16.6 billion last year in 2009, with UK residents’ expenditure abroad falling by £5.1 billion due to the current economic climate.
The number of overseas travellers visiting London during their stay here fell by 3.7% in 2009, with visits to Scotland rising slightly during this time. Edinburgh, Manchester and Birmingham remain popular destinations for overseas visitors to the UK.
The most common reason for British residents travelling abroad is still for annual holidays. They also dominate spending with £21.8 billion of the £31.7 billion total expenditure abroad in 2009 being for holiday purposes.
Throughout 2009 Egypt, Jamaica and Lithuania received an increase in visits from UK residents, continuing the overall trend in recent years. Mexico was exempt from this increase as visitors there dropped substantially by 41%.
UK residents may be taking fewer beach holidays abroad but there has been a rise in the duration of holidays in recent years. In 2007 the average stay was 9.9 nights rising to 10.2 nights in 2008 and even further to 10.5 nights in 2009.
This shows that although holidaymakers are cutting back on the amount of foreign trips they are taking, many are making up for this by increasing the time that they spend away on holiday.
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