### Table 13: Skills for which respondents apos; graduate education in mathematics was rated \less than good quot;.

"... In PAGE 22: ....6, much of the value of industrial mathematicians depends on these skills. Hence graduate education in mathematics is highly successful in preparing students for many key elements of nonacademic jobs. Table13 lists the qualities for which more than 30% of the Ph.D.... ..."

### Table 1 Knowledge, Skill, and Process Attributes Derived to Explain Performance on Mathematics Items From the TIMSS-R (1999) for Population 2 (Eighth Graders)

"... In PAGE 7: ... Tatsuoka, Corter, amp; Guerrero (2004). The set of attributes we developed fall into three general categories: content knowledge variables, cognitive process variables, and what we term skill or item-type variables ( Table1 ). The content attributes we used are not unlike the content categories used in the TIMSS-R test framework.... In PAGE 9: ...ach analysis, we used data from only Booklets (i.e., forms) 1, 3, 5, and 7, because the other booklets showed a patchy distribution of attributes (that is, few or no items measuring certain attributes). Still, we found an insuffi- cient number of items representing some of the attributes (C6, S1, S9, and P8) described in Table1 . Because this data sparseness means we cannot esti- mate these attributes reliably, they were not included in the RSM analysis.... ..."

### Table 8; also see Table 9. It is evident that many of these positions require a variety of mathematical knowledge.

"... In PAGE 16: ... Table8 : Percentages of mathematicians surveyed who mentioned mathematical specialties as a primary technical requirement of their positions; multiple mentions were permitted. Possession of broad mathematical skills is valued in nonacademic settings because technical problems driven by business needs can change rapidly, unpredictably, and dramatically, and because the work of some groups cuts across many elds.... ..."

### Table 12: Skills for which respondents apos; graduate education was rated \excellent quot; or \very good quot;.

"... In PAGE 22: ...D. apos;s are given in Table12 . Except for \creating new ideas or innovative approaches quot;, educational preparation in these qualities was also highly rated by the master apos;s graduates.... In PAGE 23: ...his set of weaknesses in graduate training is signi cant because Sections 3.1 and 3.3{ 3.5 show that these skills, in addition to those shown in Table12 , are crucial for success in nonacademic careers.... In PAGE 25: ...1. Graduate education Graduate education in mathematics serves its students well today in providing the skills from Table12 : thinking logically, dealing with complexity, conceptualizing, formulating problems, modeling, and creating new ideas.... ..."

### Table 12: Skills for which respondents apos; graduate education was rated \excellent quot; or \very good quot;.

"... In PAGE 22: ...D. apos;s are given in Table12 . Except for \creating new ideas or innovative approaches quot;, educational preparation in these qualities was also highly rated by the master apos;s graduates.... In PAGE 23: ...his set of weaknesses in graduate training is signi cant because Sections 3.1 and 3.3{ 3.5 show that these skills, in addition to those shown in Table12 , are crucial for success in nonacademic careers.... In PAGE 25: ...1. Graduate education Graduate education in mathematics serves its students well today in providing the skills from Table12 : thinking logically, dealing with complexity, conceptualizing, formulating problems, modeling, and creating new ideas.... ..."

### Table 1: Distribution across ve major industry sectors of participants in telephone survey of graduates, broken down by terminal degree. Mathematicians and their managers were asked in the telephone survey about the status of advanced mathematics in their overall organizations, where \advanced quot; means at the level of the respondent apos;s highest degree. Those responses are summarized in Table 2 and show the consistent importance of mathematics not only for its practitioners, but also for their managers. Importance of advanced mathematics Ph.D. Master apos;s Managers

"... In PAGE 9: ... (See the Appendix for more information about the survey sample.) Table1 shows the distribution of graduates surveyed in ve major sectors of industry, based on the Standard Industry Classi cation codes of the United States O ce of Management and... In PAGE 17: ...D. Master apos;s Managers Essential 54% 31% 65% Very important 28% 24% 19% Somewhat important 12% 15% 8% Not particularly important 7% 31% 8% Table1 0: Perceived importance of advanced computation. The most valued computational skills obviously depend on the context and cannot be pre- scribed in advance.... In PAGE 22: ...repared them for their jobs. The ndings of our study show an interesting mixture of opinions. Certain aspects of graduate education are almost universally praised, whereas others are widely regarded as needing improvement. As shown in Table1 1, industrial mathematicians interviewed by telephone mostly believed that their graduate education had helped them to obtain and perform well in their present positions. E ectiveness of mathematics graduate education Ph.... In PAGE 22: ...D. Master apos;s Obtaining a highly desirable position Extremely e ective 58% 57% Somewhat e ective 25% 23% Not particularly e ective 17% 20% Helping in your work Extremely e ective 59% 38% Somewhat e ective 32% 41% Not particularly e ective 9% 21% Providing a superior career path Extremely e ective 27% 18% Somewhat e ective 51% 58% Not particularly e ective 22% 24% Table1 1: Ratings of e ectiveness of graduate education in mathematics. The mathematicians surveyed were asked to rate how well their graduate education had provided them with speci c skills.... In PAGE 23: ...D. Master apos;s Working well with colleagues 67% 60% Communicating at di erent levels 58% 48% Having broad scienti c knowledge 47% 37% E ectively using computer software and systems 45% 42% Dealing with a wide variety of problems 35% 29% Table1 3: Skills for which respondents apos; graduate education in mathematics was rated \less than good quot;. This set of weaknesses in graduate training is signi cant because Sections 3.... In PAGE 23: ...his set of weaknesses in graduate training is signi cant because Sections 3.1 and 3.3{ 3.5 show that these skills, in addition to those shown in Table1 2, are crucial for success in nonacademic careers.... In PAGE 23: ... Each manager in the telephone survey was asked to indicate areas in which graduate ed- ucation in mathematics needs improvement; the six leading replies are shown in Table 14. Area for improvement in graduate mathematics education Percentage of managers Applications of mathematics 40% Knowledge of other disciplines 23% Real-world problem-solving 21% Communication; technical writing 19% Computer skills 13% Teamwork 8% Table1 4: Areas in graduate education suggested by managers as needing improvement. More than one area could be named by each manager.... In PAGE 24: ...D. Master apos;s Extremely or very important 60% 69% Somewhat important 34% 26% Not important 6% 5% Table1 5: Importance of changes in graduate mathematics education. To summarize, our inquiries indicate that graduate education in mathematics is seen by recent graduates working in industry as excellent in certain areas, but needing improvement in others.... In PAGE 25: ...1. Graduate education Graduate education in mathematics serves its students well today in providing the skills from Table1 2: thinking logically, dealing with complexity, conceptualizing, formulating problems, modeling, and creating new ideas.... In PAGE 34: ...D. Master apos;s Total number of graduates 3,701 17,780 Estimated number of graduates in industry 925 7,823 Entries in MII database 335 271 Telephone interviews 101 102 Table1 6: Ph.... ..."

### Table 2 Mathematical Software Packages Utilized Mathematical

1999

"... In PAGE 4: ... Problem originally suggested by H. S. Fogler of the University of Michigan ** Problem preparation assistance by N. Brauner of Tel-Aviv University MATHEMATICAL PACKAGES USED IN THE COMPARISON Table2 lists the various mathematical software packages that were used in the solutions to the problem set and the individuals who kindly provided the solution set. These individuals had considerable experience with the software package that they utilized.... ..."

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### Table 1. Mathematical notations.

"... In PAGE 3: ...o interaction between peers. Note that we only have one ISP in our model. The issues of multiple ISPs and multihoming are much more complicated and will appear in our future work. Lastly, Table1 contains all notations used in our mathematical model. Let a39a40a27a30a29 denote the traffic demand (or transmission rate in unit of Mbps) from peer a2 to peer a31 .... ..."

### Table I. Mathematical Notations

2005

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