{"title":"Visual Application of Sin(θ 1 + θ 2 ) = Sin θ 1 Cos θ 2 + Cos θ 1 Sin θ 2","authors":"Gerald E. Gannon","doi":"10.2307/3027392","DOIUrl":"https://doi.org/10.2307/3027392","url":null,"abstract":"","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117318318","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":"Teachers, Clocks, and Students.","authors":"S. Stein","doi":"10.2307/3027389","DOIUrl":"https://doi.org/10.2307/3027389","url":null,"abstract":"Since receiving his Ph.D. at Columbia, Sherman Stein has maintained his interests in both research, primarily in algebra, ,iC/Y Ods N and teaching. He has written two college texts, \"Mathematics, /->5 S~xflS, the Man-made Universe\" and \"Calculus and Analytic Geometry.\" With Calvin Crabill and G. Donald Chakerian, he developed a series of three high school texts adapted to both the g 3 7a'9lecture and small-group approach, covering introductory algebra, geometry, and algebra 2-trigonometry. His expository article, \"Algebraic Tiling,\" earned the Lester R. Ford award in 1974.","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126453827","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":"Guessing an Algorithm--A Case for Interpolation.","authors":"D. R. Lichtman","doi":"10.2307/3027390","DOIUrl":"https://doi.org/10.2307/3027390","url":null,"abstract":"","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129396138","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":"The Nature of Proof: Limits and Opportunities","authors":"K. Appel, W. Haken","doi":"10.2307/3027373","DOIUrl":"https://doi.org/10.2307/3027373","url":null,"abstract":"The fundamental reason that the unavoidable set argument worked whereas other approaches to the Four-Color Conjecture did not is that all other approaches need somewhat stronger theoretical tools to make their methods apply. While these might be possible to create, there is no guarantee that they are actually possible; and if they are, there is no obvious way to go about finding them. On the other hand, many mathematicians have believed that an unavoidable set of reducible configurations might exist, but that a smallest such set was beyond the bounds of reasonable computation. This attitude appears justified when the problem is considered with respect to the tools available prior to 1960. After 1960, with the advent of faster computers, there were still strong reasons to believe that the computations would be infeasibly large, but there were certainly no theoretical difficulties to overcome other than the choice of a method for obtaining an unavoidable set. Thus by 1970 it became a problem of discovering whether efficient use of known techniques and technical (as opposed to theoretical) improvements would enable one to find an unavoidable set of reducible configurations. Most mathematicians who were educated prior to the development of fast computers tend not to think of the computer as a routine tool to be used in conjunction with other older and more theoretical tools in advancing mathematical knowledge. Thus they intuitively feel that if an argument contains parts that are not verifiable by hand calculations it is on rather insecure ground. There is a tendency to feel that verification of computer results by independent computer programs is not as certain to be correct as independent hand checking of the proof of theorems proved in the standard way.","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134182625","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":"Partial and Semipartial Correlation-A Vector Approach","authors":"John C. Huber","doi":"10.2307/3027381","DOIUrl":"https://doi.org/10.2307/3027381","url":null,"abstract":"","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129286391","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":"Polite Applause for a Proof of One of the Great Conjectures of Mathematics: What Is a Proof Today?","authors":"D. Albers","doi":"10.2307/3027369","DOIUrl":"https://doi.org/10.2307/3027369","url":null,"abstract":"","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"9 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114006947","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":"An Informal History of Formal Proofs: From Vigor to Rigor?.","authors":"K. Galda","doi":"10.2307/3027375","DOIUrl":"https://doi.org/10.2307/3027375","url":null,"abstract":"This paper pretends to cover a subject in a few pages which could not be adequately covered in a thousand pages. Therefore, in the interest of brevity and readability the reader should realize that we will lose completeness, accuracy, and possibly consistency. (The loss of consistency would at least ensure completeness, albeit in an","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132644947","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":"Distance from a Point to a Line","authors":"K. Sastry","doi":"10.2307/3027378","DOIUrl":"https://doi.org/10.2307/3027378","url":null,"abstract":"","PeriodicalId":448750,"journal":{"name":"Two-Year College Mathematics Journal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1981-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122390704","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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