{"title":"Problems and Solutions","authors":"Greg Oman, Charles N. Curtis","doi":"10.1080/07468342.2023.2202077","DOIUrl":"https://doi.org/10.1080/07468342.2023.2202077","url":null,"abstract":"This section contains problems intended to challenge students and teachers of college mathematics. We urge you to participate actively both by submitting solutions and by proposing problems that are new and interesting. To promote variety, the editors welcome problem proposals that span the entire undergraduate curriculum. Proposed problems should be uploaded to the submission management system Submittable by visiting the web address https://cmj.submittable.com/submit (instructions are provided at this site). Alternatively, problem proposals may be sent to Greg Oman, either by email (preferred) as a pdf, TEX, or Word attachment or by mail to the address provided above. Whenever possible, a proposed problem should be accompanied by a solution, appropriate references, and any other material that would be helpful to the editors. Proposers should submit problems only if the proposed problem is not under consideration by another journal. Solutions to the problems in this issue should be uploaded to the submission management system Submittable by visiting the web address https://cmj.submittable.com/submit (instructions are provided at this site). Alternatively, solutions may be sent to Chip Curtis, either by email as a pdf, TEX, or Word attachment (preferred) or by mail to the address provided above, no later than September 15, 2023. Sending both pdf and TEXfiles is ideal.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"236 - 242"},"PeriodicalIF":0.0,"publicationDate":"2023-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47474130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"How to Fold a Triangle: The Connection between the Grashof Fourbar Linkage and Pythagorean Triangles","authors":"E. Constans, Nicola Golfari","doi":"10.1080/07468342.2023.2213156","DOIUrl":"https://doi.org/10.1080/07468342.2023.2213156","url":null,"abstract":"","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47599261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Rebalance Your Portfolio Without Selling","authors":"J. Bartroff","doi":"10.1080/07468342.2023.2228671","DOIUrl":"https://doi.org/10.1080/07468342.2023.2228671","url":null,"abstract":"Summary How do you bring your assets as close as possible to your target allocation by only investing a fixed amount of additional funds, and not selling any assets? We look at two versions of this problem which have simple, closed form solutions revealed by basic calculus and algebra.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"290 - 298"},"PeriodicalIF":0.0,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43064030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Proof Without Words: Lagrange’s Trigonometric Identity (Part II)","authors":"J. Balsam","doi":"10.1080/07468342.2023.2206782","DOIUrl":"https://doi.org/10.1080/07468342.2023.2206782","url":null,"abstract":"Summary Lagrange’s Trigonometric Identity is usually proven analytically by summing a geometric series in the complex numbers. This Proof Without Words is purely geometric.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"235 - 235"},"PeriodicalIF":0.0,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47927607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Balancing the Square Root of Two","authors":"Tom Edgar","doi":"10.1080/07468342.2023.2201569","DOIUrl":"https://doi.org/10.1080/07468342.2023.2201569","url":null,"abstract":"Summary We give a physical proof, using moments of mass, that the square root of two is irrational.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"176 - 178"},"PeriodicalIF":0.0,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45736593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modifying Jordan Bases","authors":"Grega Cigler, Marjan Jerman","doi":"10.1080/07468342.2023.2201146","DOIUrl":"https://doi.org/10.1080/07468342.2023.2201146","url":null,"abstract":"Summary In linear algebra classes we usually teach our students how to find a basis relative to which a Jordan matrix corresponds to an endomorphism of a finite dimensional space. Here we look at this problem from a different perspective. Suppose that we have a Jordan basis. How do we get all other Jordan bases from this existing basis?","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"222 - 231"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48964339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Improper Integrals: An Alternative Criterion","authors":"Katiuscia C. B. Teixeira","doi":"10.1080/07468342.2023.2201566","DOIUrl":"https://doi.org/10.1080/07468342.2023.2201566","url":null,"abstract":"Katiuscia Teixeira (katiuscia.teixeira@ucf.edu), University of Central Florida. The topic Improper Integrals, often introduced in the second course of Calculus, is an important, though difficult concept for students to grasp, viz. [1–3]. In this article we discuss an alternative (geometric) criterion for an improper integral to diverge. While the criterion is indeed efficient and easy to apply, if one believes, like I do, that teaching Calculus is more than training students to manipulate formulas, then the opportunity to present and discuss the reasoning leading to such a result should be thought as more valuable than the criterion, per se. Let us start off with a classical example of divergent integral: ∫ 1","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"232 - 234"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48138730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Trigonometric Angle-Sum Formulas and Conformal Maps","authors":"Greg Markowsky, David Treeby","doi":"10.1080/07468342.2023.2201563","DOIUrl":"https://doi.org/10.1080/07468342.2023.2201563","url":null,"abstract":"Summary The trigonometric angle-sum formulas are given a new interpretation as statements about conformal maps. In particular, we show how the angle-sum formula for tangent can be realized by equating two different conformal maps from an infinite strip to a disk, and the formulas for sine and cosine by similarly equating conformal maps from an infinite strip to a certain slit domain.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"195 - 199"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45134188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Knot Theory in Linear Algebra: An Example with Trip Matrices","authors":"Molly A. Moran, Jessica Schenkman","doi":"10.1080/07468342.2023.2201163","DOIUrl":"https://doi.org/10.1080/07468342.2023.2201163","url":null,"abstract":"Summary The trip matrix, introduced by Louis Zulli [6], gives a method for computing the Jones polynomial of a knot using basic Linear Algebra. We use this method to provide an alternative proof of the formula for the Jones polynomial of torus knots. In doing so, we provide a partial solution to an open question related to finding an elementary proof of the formula for general torus knots.","PeriodicalId":38710,"journal":{"name":"College Mathematics Journal","volume":"54 1","pages":"186 - 194"},"PeriodicalIF":0.0,"publicationDate":"2023-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49022306","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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