Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics.

Number theory (or arithmetic) is a branch of pure mathematics devoted primarily to the study of the integers, sometimes called "The Queen of Mathematics" because of its foundational place in the discipline. Number theorists study prime numbers as well as the properties of objects made out of integers or defined as generalizations of the integers.

Algebraic geometry is a branch of mathematics, classically studying zeros of polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.[read more at Algebra, Number Theory, Algebraic Geometry wiki pages ]

### Academic Factors Comparison Between Best Colleges in Algebra / Number Theory / Algebraic Geometry Major

3 public and 7 private schools are ranked in the top 10 Algebra / Number Theory / Algebraic Geometry colleges. The average acceptance ratio of the schools is 11.00% where Harvard University has the tightest acceptance ratio of 5% and University of Michigan-Ann Arbor has the highest ratio of 29%. Total 252,674 students are enrolled into best Algebra / Number Theory / Algebraic Geometry schools where University of Michigan-Ann Arbor has the largest population with 44,718 students and Princeton University has the smallest with 8,181 students. The average graduation rate is 94.10% and the average students to faculty ratio is 9.00:1 at those colleges.

Next table shows the academic information and key facts of the best Algebra / Number Theory / Algebraic Geometry colleges including acceptance ratio, graduation rates, student population, and students to faculty ratio.Rank | Name | Acceptance Rates | Graduation Rates | Population | Student-Faculty Ratio |
---|---|---|---|---|---|

1 | Harvard University Cambridge, MA | 5% | 97% | 29,908 | 7:1 (14.29 %) |

2 | Princeton University Princeton, NJ | 7% | 97% | 8,181 | 5:1 (20.00 %) |

3 | University of California-Berkeley Berkeley, CA | 17% | 92% | 40,154 | 18:1 (5.56 %) |

4 | University of Chicago Chicago, IL | 8% | 94% | 15,775 | 6:1 (16.67 %) |

5 | Massachusetts Institute of Technology Cambridge, MA | 8% | 93% | 11,376 | 3:1 (33.33 %) |

5 | University of California-Los Angeles Los Angeles, CA | 18% | 91% | 43,548 | 17:1 (5.88 %) |

7 | Stanford University Stanford, CA | 5% | 94% | 17,184 | 10:1 (10.00 %) |

8 | University of Michigan-Ann Arbor Ann Arbor, MI | 29% | 91% | 44,718 | 12:1 (8.33 %) |

9 | Columbia University in the City of New York New York, NY | 7% | 94% | 29,372 | 6:1 (16.67 %) |

10 | Yale University New Haven, CT | 6% | 98% | 12,458 | 6:1 (16.67 %) |

Average | 11.00% | 94.10% | 252,674 (Total) | 9.00:1 (11.11 %) |

### Best Algebra / Number Theory / Algebraic Geometry Colleges 2018 Tuition & Fees Comparison and 2019 Estimated Costs

Next table lists 2017-2018 tuition & fees and compares the costs between Best Algebra / Number Theory / Algebraic Geometry 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 Algebra / Number Theory / Algebraic Geometry schools is $49,118 where Columbia University in the City of New York has the most expensive costs with $57,208 and University of California-Los Angeles has the lowest amount of tuition with with $41,275. The average graduate tuition & fees of best Algebra / Number Theory / Algebraic Geometry schools is $44,355 where University of Chicago has the highest tuition with $57,000 and University of California-Los Angeles has the lowest amount of tuition with with $28,105.

Top Algebra / Number Theory / Algebraic Geometry Schools Admission and Tuition Comparison

Rank | School Name | 2018 Tuition & Fees | 2019 Estimated Tuition & Fees | ||
---|---|---|---|---|---|

In-State | Out-of-State | In-State | Out-of-State | ||

1 | Harvard University | $48,949 | $50,898 | ||

2 | Princeton University | $47,140 | $49,054 | ||

3 | University of California-Berkeley | $14,170 | $42,184 | $14,863 | $44,276 |

4 | University of Chicago | $56,034 | $59,816 | ||

5 | Massachusetts Institute of Technology | $49,892 | $51,374 | ||

5 | University of California-Los Angeles | $13,261 | $41,275 | $13,611 | $43,019 |

7 | Stanford University | $49,617 | $51,352 | ||

8 | University of Michigan-Ann Arbor | $14,826 | $47,476 | $14,357 | $47,953 |

9 | Columbia University in the City of New York | $57,208 | $59,444 | ||

10 | Yale University | $51,400 | $53,394 | ||

Average | $14,086 | $49,118 | $14,277 | $51,058 |

Rank | School Name | 2018 Tuition & Fees | 2019 Estimated Tuition & Fees | ||
---|---|---|---|---|---|

In-State | Out-of-State | In-State | Out-of-State | ||

1 | Harvard University | $45,958 | $47,587 | ||

2 | Princeton University | $48,940 | $50,722 | ||

3 | University of California-Berkeley | $14,170 | $29,272 | $14,863 | $29,948 |

4 | University of Chicago | $57,000 | $59,245 | ||

5 | Massachusetts Institute of Technology | $52,892 | $54,588 | ||

5 | University of California-Los Angeles | $13,003 | $28,105 | $13,331 | $28,429 |

7 | Stanford University | $47,940 | $47,940 | ||

8 | University of Michigan-Ann Arbor | $22,696 | $45,484 | $23,635 | $47,369 |

9 | Columbia University in the City of New York | $46,956 | $48,401 | ||

10 | Yale University | $41,000 | $42,236 | ||

Average | $16,623 | $44,355 | $17,277 | $45,647 |

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