What Is Real Analysis in Economics

What do you learn in a real analysis course? What do you need to know before you take a real analysis course? Why is taking a real analysis course helpful if you’re planning to do graduate work in economics? There are a lot of questions that might be running through your head if youre unfamiliar with real analysis or havent actually taken a real analysis course. What Is Taught in a Real Analysis Course We can get a feel for what is taught in a real analysis course by taking a look at a couple of real analysis course descriptions. Here’s one from Margie Hall at Stetson University: Real analysis is a large field of mathematics based on the properties of the real numbers and the ideas of sets, functions, and limits. It is the theory of calculus, differential equations, and probability, and it is more. A study of real analysis allows for an appreciation of the many interconnections with other mathematical areas. A slightly more complex description is given by Steve Zelditch at Johns Hopkins University: Real Analysis is an enormous field with applications to many areas of mathematics. Roughly speaking, it has applications to any setting where one integrates functions, ranging from harmonic analysis on Euclidean space to partial differential equations on manifolds, from representation theory to number theory, from probability theory to integral geometry, from ergodic theory to quantum mechanics. As you can see, real analysis is a somewhat theoretical field that is closely related to mathematical concepts used in most branches of economics such as calculus and probability theory. Common Prerequisites of Real Analysis To be comfortable in a real analysis course, you should have a good background in calculus first. In the book Intermediate Analysis John M.H. Olmstead recommends taking real analysis fairly early in one’s academic career: ...a student of mathematics should properly begin to make his acquaintance with the tools of analysis as soon as possible after the completion of the first course in calculus There are two key reasons why those entering a graduate program in economics should have a strong background in real analysis: Topics covered in real analysis, such as differential equations and probability theory are used extensively in economics.Graduate students in economics will commonly be asked to write and understand mathematical proofs, skills which are taught in real analysis courses. Prof. Olmstead saw practicing proofs as one of the core objectives of any real analysis course: In particular, the student should be encouraged to prove (in full detail) statements which previously he has been persuaded to accept because of their immediate obviousness. Thus, if a real analysis course is not available at your college or university, we highly recommend taking a course in how to write mathematical proofs, which the mathematics departments of most schools offer.

Pain Case Study - 965 Words

The objective of the study was to compare the incidence of post-operative pain between rotary andhand K-files single visit root canal treatment. 60 patients with symptomatic irreversible pulpitis participated in this randomized clinical trial at Altamash Dental Institute from Sep 2016 to May 2017. Patients were randomly alienated into 2 distinct groups of 30 patients. Single visit root canal treatment were perfomed by cleaning and shaping of canals by means of rotary files in group A while in group B hand K-files were used for shaping and cleaning via passive step-back technique followed by obturation and termporary filling on the same visit. Following the treatment, patients were directed to compute pain intensity at 4, 8, 12 and 24†¦show more content†¦It is evaluated from former studies that technique in which instrument is used in rotational manner tends to extrude reduce amount of debris in apical region in contrast to technique that uses up and down stroke. Likewise, custom-hand filing technique is more conscientious for debris extrusion than motor-driven files. Further, flutes in rotary files have more propensities to haul the debris coronally (9, 10, 13, 15, and 18). According to most of the studies, hand instruments cause more post-operative pain in comparison to NiTi rotary files (17-22). However, according to a newstudy, no significant difference in post-operative pain was noticed with different instrumentation (23). Instrumentation shares no relationship with post-endodontic pain, as evaluated from prior studies (24). According to researchers, numbers of visit shares no association with post-endodontic pain (25-30). However, according to some studies RCT performed in multiple visits results in elevated post-operative pain (31-32). Similarly, another study states that patients treated in single visit are more likely to undergo post-operative pain (33-36). METHODOLOGY This randomized clinical trialwas conducted at Altamash Dental Institute from Sep 2016 to May 2017.60 patients were selected by convenience sampling. Informed verbalShow MoreRelatedPain Case Study1014 Words   |  5 Pagesper day and uses recreational grade cannabis for pain and sleep daily. On admission, Ms. Kelly complained of low back pain ranging in intensity from 7 to 8, out of 10, on the pain scale where 0 is no pain and 10 is the worst imaginable pain. She subjectively describes this pain as throbbing, stabbing, burning and radiating along the posterior and anterior aspect of both upper legs, left worse than right. She has sharp, stabbing, burning pain in both her arms, particularly the left arm, andRead MorePain Case Study1732 Words   |  7 Pages Pain is often related to increased anxiety, sleep disorder, depression and lower quality of life (Tsao, Plankey Young, 2012). According to Beavers, Giggey Tepe (2009), the prevalence of chronic pain together with a mental disorder is 30%, which doubles the percentage of individuals without a mental disorder. Sun et al. (2013) compared the therapeutic effects of electroacupuncture and fluoxetine on the depressive disorder (MDD). The study demonstrated that electroacupuncture treatmentRead MoreNeuropathic Pain Case Study1773 Words   |  8 PagesMany clinical conditions require bone or tissue regeneration and current therapeutic options (pharmacotherapy, neurosurgical lesioning, and anesthetic blocks) do not provide effective long-term relief associated with the accompanied neuropathic pain. Regenerative therapy uses a patient’s own tissues to initiate the healing process. Two regenerative treatments currently being offered are stem cell and platelet-rich plasma therapy. The use of adult stem cells for bone and tissue regeneration has gainedRead MoreTemporomandibular Joint Pain Case Study1056 Words   |  5 PagesResult s The current study was conducted on nineteen patients 3 males (15.7%) and 16 females (84.28 %) with mean age 26.26 years  ± 6.24. Evaluation of temporomandibular joint pain by visual analogue scale VAS during joint function was calculated by the statistical change in reference to the preoperative records. Results revealed that the reduction in TMJ pain was statistically significant after the first week (P=0.002) and the reduction in pain was improved along the study period till the 6th monthRead MoreCase Study Of Phantom Pain ( Phantom Limb Pain ( PLP )1006 Words   |  5 PagesPhantom pain (Phantom limb pain [PLP]) PLP is one of those strange afflictions of the human body which can be caused by a number of instances. Although surgery and the removal of limbs, hence the name, are the primary and most common way of developing PLP, there are numerous other ways which can bring PLP on, albeit not in as severe ways; these ways include, but are not limited to Touch, Urination or defecation, Sexual intercourse, Angina, Cigarette smoking, Changes in barometric pressure, HerpesRead MoreCase Study : Au Bon Pain1194 Words   |  5 PagesAt Au Bon Pain (ABP), Ron Shaich, company President hired Len Schlesinger as Executive Vice President/Treasurer to increase sales and improve quality. They recognized store performance and customer service were degrading from the phenomenon they called â€Å"the cycle of failure† caused by chronic employee shortage, inability to recruit high performing managers and insufficient training. Ron/Len identified that a new competitive compensation program (pay for perf ormance) at the manager level could createRead MorePerineal Pain In Nursing Case Study712 Words   |  3 PagesThe current study findings indicated that perineal pain intensity had significantly reduced 15 minutes after the warm compresses and after lubricated massage among the two intervention groups (P = 0.000) with more effect to the lubricated massage. Meanwhile, perineal pain intensity had increased among the control group after received routine care (P =0.000). With statistically significant differences between the two intervention groups and control group regarding perineal pain intensity after interventionRead MoreCharacteristics Of Caring For Patients1231 Words   |  5 PagesAnother positive consequence is a feeling of power and autonomy for patients. Finally, the patient’s perception of the nurse is positively influenced as they are now viewed as compassionate, competent, and respectful (Brilowski Wendler, 2005). Cases Model Case #1 Mr. Smith, a 72 year old man has been admitted to an orthopedic floor following the surgical repair of a fractured femur. Ann, his nurse, knows that Mr. Smith is a type II diabetic, has a history of hypertension, DVT, a-fib, and two cardiacRead MoreThe Treatment of Phobias Essay851 Words   |  4 Pagesof injections. Several people today suffer from travel phobia, yet there is little data regarding the phobia. The purpose of this study was to review the usefulness of a trauma-focused treatment approach for travel phobia from a cognitive behavioral therapy. Such technique used for the study was Eye Movement Desensitization and Reprocessing (EMDR) for a 184 person case from a rehabilitation provider. The reasoning for these particular tests was to enact a full body approach where as it tested allRead More`` Not For Iv Use : The Story Of An Enteral Tubing Misconnection1143 Words   |  5 PagesChosen for root cause analysis is case study number 18, titled â€Å"Not for IV Use: The Story of an Enteral Tubing Misconnection† from the book Case Studies in Patient Safety: Foundations for Core Competencies. Root cause analysis is a process whereby error producing system factors are identified and reviewed to assist in the formatting and implementation of solutions to prevent similar errors from re occurrence (Wachter, 2012). This accounting of the patient’s experience located in the Systems-Based

Frankenstein vs Planet of the Apes Free Essays

Frankenstein VS Planet of the Apes: A Frightful Showdown Humans as a species like to experiment with the world around them and push the limits of any known law. As a result, the human race is constantly toying with the everlasting puzzle: What is life and how can it be manipulated? Through many realistic fiction stories—such as Mary Shelley’s Frankenstein and Rise of the Planet of the Apes—the general public is able to take a look into how far the human mind wants to go. Both stories use technology as a vehicle to enhancing human life and end up with horrible endings. We will write a custom essay sample on Frankenstein vs Planet of the Apes or any similar topic only for you Order Now Though these tales share a common theme, they diverge in plot lines by exploring different ways that technology can affect life as usual. By examining these tales one will notice the difference of experiments, consequences, and relationships. The first major difference is the means of experimentation between the two protagonists. In Frankenstein, Victor uses a mysterious â€Å"spark of life† to bring his creation alive in order to fulfill his own ambitions. In Rise of the Planet of the Apes, the protagonist’s motivation for experimenting on life is for the greater good from the get go. By these plots being different, the audience can see how even though scientists can have totally separate ideas and reasoning the end game is usually the same. However, this was not the only difference between the cautionary narratives. The other key thing that made these stories different was the endings. In the film, the experiments wreak havoc on the city just so that they could get to safety. In the novel, the creation causes destruction for the sole purpose of tormenting its creator. The apes reach their destination and though they leave a wake of terror in their path are generally safe and complacent, while the protagonist quietly mourns losing his friend. On the other hand, Victor loses his life in the hunt for the creation and the monster commits suicide leaving no trace of any the events that took place. These two differences are what make each tale unique. The film and novel have one commonality: they warn humans of the dangers that can be self-inflicted. Each story results in suffering, loss, and destruction caused by the creations. They try and convey the message that manipulating life can be a volatile process and should be handled with the utmost care. Though one lead character lives while the other main character dies, they both reach a point where they realize the power and seriousness of their actions therefore teaching the reader/ viewer. Watching/ reading these interesting narratives can leave a person more cautious of their actions and decisions. Overall, the book and film differed in a variety of ways, ways such as plot line and end results. However the overall theme of the power of technology in human lives remained dominant in both tales. One is a film with wonderful visual effects and the other is an aged book that still retains the vividness of its day. They are both striking entertainment and could be interchangeable for instilling a sense of power and responsibly in reckless youth. There were few things that could be tweaked and more informative tales should be made revolving around this universal subject. How to cite Frankenstein vs Planet of the Apes, Papers