Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics - such as integers, graphs, and statements in logic - do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable sets (sets that have the same cardinality as subsets of the natural numbers, including rational numbers but not real numbers). However, there is no exact, universally agreed, definition of the term "discrete mathematics." Indeed, discrete mathematics is described less by what is included than by what is excluded: continuously varying quantities and related notions.[read more at wiki]
Academic Factors Comparison Between Best Colleges in Discrete Mathematics And Combinatorics Major
8 public and 2 private schools are ranked in the top 10 Discrete Mathematics and Combinatorics colleges. The average acceptance ratio of the schools is 30.20% where Princeton University has the tightest acceptance ratio of 7% and University of Illinois at Urbana-Champaign has the highest ratio of 60%. Total 358,471 students are enrolled into best Discrete Mathematics and Combinatorics schools where University of Minnesota-Twin Cities has the largest population with 51,579 students and Princeton University has the smallest with 8,181 students. The average graduation rate is 88.00% and the average students to faculty ratio is 14.60:1 at those colleges.
Next table shows the academic information and key facts of the best Discrete Mathematics and Combinatorics colleges including acceptance ratio, graduation rates, student population, and students to faculty ratio.| Rank | Name | Acceptance Rates | Graduation Rates | Population | Student-Faculty Ratio |
|---|---|---|---|---|---|
| 1 | Massachusetts Institute of Technology Cambridge, MA | 8% | 93% | 11,376 | 3:1 (33.33 %) |
| 2 | Princeton University Princeton, NJ | 7% | 97% | 8,181 | 5:1 (20.00 %) |
| 3 | University of California-San Diego La Jolla, CA | 36% | 87% | 34,979 | 19:1 (5.26 %) |
| 4 | Georgia Institute of Technology-Main Campus Atlanta, GA | 26% | 86% | 26,839 | 20:1 (5.00 %) |
| 5 | University of Michigan-Ann Arbor Ann Arbor, MI | 29% | 91% | 44,718 | 12:1 (8.33 %) |
| 6 | University of California-Berkeley Berkeley, CA | 17% | 92% | 40,154 | 18:1 (5.56 %) |
| 6 | University of California-Los Angeles Los Angeles, CA | 18% | 91% | 43,548 | 17:1 (5.88 %) |
| 8 | Rutgers University-New Brunswick New Brunswick, NJ | 57% | 80% | 50,146 | 15:1 (6.67 %) |
| 8 | University of Illinois at Urbana-Champaign Champaign, IL | 60% | 85% | 46,951 | 20:1 (5.00 %) |
| 8 | University of Minnesota-Twin Cities Minneapolis, MN | 44% | 78% | 51,579 | 17:1 (5.88 %) |
| Average | 30.20% | 88.00% | 358,471 (Total) | 14.60:1 (6.85 %) |
Best Discrete Mathematics and Combinatorics Colleges 2018 Tuition & Fees Comparison and 2019 Estimated Costs
Next table lists 2017-2018 tuition & fees and compares the costs between Best Discrete Mathematics and Combinatorics Colleges. The 2017-2018 costs are officially published by IPEDS, U.S. Department of Education. The estimated costs for year 2018-2019 are calculated and estimated based on each school's tuition rates last year.
For the undergraduate programs, the average tuition & fees of best Discrete Mathematics and Combinatorics schools is $39,139 where Massachusetts Institute of Technology has the most expensive costs with $49,892 and University of Minnesota-Twin Cities has the lowest amount of tuition with with $26,603. The average graduate tuition & fees of best Discrete Mathematics and Combinatorics schools is $35,345 where Massachusetts Institute of Technology has the highest tuition with $52,892 and University of Minnesota-Twin Cities has the lowest amount of tuition with with $27,388.
| Rank | School Name | 2018 Tuition & Fees | 2019 Estimated Tuition & Fees | ||
|---|---|---|---|---|---|
| In-State | Out-of-State | In-State | Out-of-State | ||
| 1 | Massachusetts Institute of Technology | $49,892 | $51,374 | ||
| 2 | Princeton University | $47,140 | $49,054 | ||
| 3 | University of California-San Diego | $14,018 | $42,032 | $14,401 | $43,809 |
| 4 | Georgia Institute of Technology-Main Campus | $12,418 | $33,014 | $12,627 | $33,635 |
| 5 | University of Michigan-Ann Arbor | $14,826 | $47,476 | $14,357 | $47,953 |
| 6 | University of California-Berkeley | $14,170 | $42,184 | $14,863 | $44,276 |
| 6 | University of California-Los Angeles | $13,261 | $41,275 | $13,611 | $43,019 |
| 8 | Rutgers University-New Brunswick | $14,638 | $30,579 | $14,909 | $31,145 |
| 8 | University of Illinois at Urbana-Champaign | $15,074 | $31,194 | $13,223 | $28,610 |
| 8 | University of Minnesota-Twin Cities | $14,417 | $26,603 | $14,697 | $29,729 |
| Average | $14,103 | $39,139 | $14,086 | $40,261 | |
| Rank | School Name | 2018 Tuition & Fees | 2019 Estimated Tuition & Fees | ||
|---|---|---|---|---|---|
| In-State | Out-of-State | In-State | Out-of-State | ||
| 1 | Massachusetts Institute of Technology | $52,892 | $54,588 | ||
| 2 | Princeton University | $48,940 | $50,722 | ||
| 3 | University of California-San Diego | $13,085 | $28,187 | $13,085 | $28,187 |
| 4 | Georgia Institute of Technology-Main Campus | $15,798 | $30,578 | $15,945 | $31,093 |
| 5 | University of Michigan-Ann Arbor | $22,696 | $45,484 | $23,635 | $47,369 |
| 6 | University of California-Berkeley | $14,170 | $29,272 | $14,863 | $29,948 |
| 6 | University of California-Los Angeles | $13,003 | $28,105 | $13,331 | $28,429 |
| 8 | Rutgers University-New Brunswick | $18,984 | $30,792 | $19,342 | $31,370 |
| 8 | University of Illinois at Urbana-Champaign | $18,224 | $31,811 | $18,159 | $32,096 |
| 8 | University of Minnesota-Twin Cities | $18,232 | $27,388 | $18,743 | $28,183 |
| Average | $16,774 | $35,345 | $17,138 | $36,199 | |
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