TCUMath

NewsletterWe should take care not to make the intellect our god; it

has, of course, powerful muscles, but no personality.

- Albert Einstein Out of My Later Life, 1950

Vol 24 No 3 November 2015

Spring2016UpperLevelMathClassesThe TCU Mathematics Department will offer a wideselection of upper level math classes this spring. Inaddition to the classesMath 50253 Abstract Algebra Iand Math 50323 Differential Geometry, the followingwillbeoffered:Math60223/40970SurveyofMathematicalProblemsMath60323/40970AlgebraicTopologyMath60643/40970DynamicalSystemsMath60603/40970GameTheoryMath60970/40970AdvancedRealAnalysisIfyouareinterestedintheseclasses,seetheTCUcatalogdescriptionandtheprofessorsofferingtheclasses.Theplanned mathematics course offerings for the next 4yearswillbeemailedtoallmajorsandminorssoon.CareerConsultantfortheCollegeofScienceandEngineeringGabrielaMartinezhasjoinedtheTCUCenterforCareerandProfessionalDevelopmentastheCareerConsultantliaison to the College of Science and Engineering. Herhours will be from 8 am to 5 pm at the followinglocations: Jarvis, 1st floor on Monday, Wednesday,Friday, and TUC 003G on Tuesday and Thursday. Theservices she offers include résume reviews, interviewcoaching, career and personality assessments, and jobsearchstrategies.ToscheduleanappointmentwithMs.Martinez,call817-257-2222.

NovemberTCUActuarialTalksBen Hagan and TCU graduate AshNyanganiofMercerwillbethenextspeakers in theTCUActuarialTalkseries. They will present the talk“TheConsultingIndustry&Today’sRetirementChallenges”onMonday,November2at3:30pminTUC352.In this talk, you can learn what aretirementconsultingactuarydoes,The second November actuarialtalk, presented by AON,will be onMonday, November 16 at 3:30 pmin TUC 352. Refreshments will beavailable before both talks in TUC300.FrankStonesColloquiumTalkonNovember20Professor Andrew Blumberg fromthe University of Texas in Austinwill speak in Frank StonesColloquium Series on Friday,November20.Thetalkwillat3:30pm in TUC 352 with refreshrefreshmentsservedinTUCat3:00pm.

SolutiontotheOctober2015ProblemoftheMonth

Editor:RhondaHatcherProblemEditor:GeorgeGilbertThoughtoftheMonthEditor:RobertDoran

October2010ProblemoftheMont

November2015ProblemoftheMonth

Thismonth’sproblemwasMathCentral’sfinalProblemoftheMonth.Findallpairsofrealnumbers𝑎and𝑏suchthatallrootsof3𝑥! − 12𝑥 + 2𝑎 and 𝑥! − 𝑎𝑥! + 𝑏𝑥 − 8 are nonnegative realnumbers.Students and others are invited to submit solutions to Dr. George Gilbert by e-mail(g.gilbert@tcu.edu) or hard copy (Math Dept. Office or TCU Box 298900). Correct solutionssubmittedbypersonswhoarenotmembersoftheTCUmathfacultywillbeacknowledgedinthenext issue of the newsletter.Note that a correct solution is an answer and a justification of itscorrectness.Thesolutiontotheproblemwillbepublishedinthenexteditionofthenewsletter.

Problem:Showthat1− 2!! 1− 2!! ⋯ 1− 2!(!!!) 1− 2!!

isgreaterthan¼foreverypositiveinteger𝑛.Solution:(BradBeadle’96)Usetheinequality 1− 𝑎 1− 𝑏 > 1− (𝑎 + 𝑏)for 0 < 𝑎 < 1, 0 < 𝑏 < 1repeatedlyandthegeometricseriesformulatoconclude

1− 2!! 1− 2!! ⋯ 1− 2! !!! 1− 2!! =12 1−

14+

18+⋯+

12!

>12 1−

14+

18+⋯+

12! +⋯ =

12 1−

14

1− 12=14 .