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18.785 Number Theory I (MIT)

Description

This is the first semester of a one year graduate course in number theory covering standard topics in algebraic and analytic number theory. At various points in the course, we will make reference to material from other branches of mathematics, including topology, complex analysis, representation theory, and algebraic geometry.

Subjects

Absolute values | discrete valuations | localization | Dedekind domains | Etale algebras | Dedekind extensions | Ideal Norm | Dedekind-Kummer Theorem | Galois extensions | Frobenius | Artin map | complete fields | Valuation rings | Hensel's lemmas | Krasner's lemma | Haar measures | Minkowski bound | Dirichlet | Unit theorem | Riemann | Zeta function | Kronecker | Weber | Ray Class | Ring of Adeles | Idele group | Chebotarev density theorem

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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Silvia; or, the country burial. An opera: As it is performed at the Theatre-Royal in Lincoln's-Inn Fields. With the musick prefix'd to each song. Silvia; or, the country burial. An opera: As it is performed at the Theatre-Royal in Lincoln's-Inn Fields. With the musick prefix'd to each song.

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ebook version of Silvia; or, the country burial. An opera: As it is performed at the Theatre-Royal in Lincoln's-Inn Fields. With the musick prefix'd to each song. ebook version of Silvia; or, the country burial. An opera: As it is performed at the Theatre-Royal in Lincoln's-Inn Fields. With the musick prefix'd to each song.

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Enthusiasm: a poem. In two parts. By Mr. Jerningham Enthusiasm: a poem. In two parts. By Mr. Jerningham

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ebook version of Enthusiasm: a poem. In two parts. By Mr. Jerningham ebook version of Enthusiasm: a poem. In two parts. By Mr. Jerningham

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Hermione, or the orphan sisters: A novel. In four volumes. ... [pt.2] Hermione, or the orphan sisters: A novel. In four volumes. ... [pt.2]

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ebook version of Hermione, or the orphan sisters: A novel. In four volumes. ... [pt.2] ebook version of Hermione, or the orphan sisters: A novel. In four volumes. ... [pt.2]

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c. relative chiefly to picturesque beauty; made in the summer of the year 1770, second edition, by William Gilpin, ... c. relative chiefly to picturesque beauty; made in the summer of the year 1770, second edition, by William Gilpin, ...

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ebook version of Observations on the River Wye: and several parts of South Wales, &c. relative chiefly to picturesque beauty; made in the summer of the year 1770, second edition, by William Gilpin, ... ebook version of Observations on the River Wye: and several parts of South Wales, &c. relative chiefly to picturesque beauty; made in the summer of the year 1770, second edition, by William Gilpin, ...

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He's much to blame: a comedy: in five acts. As performed at the Theatre Royal, Covent Garden. He's much to blame: a comedy: in five acts. As performed at the Theatre Royal, Covent Garden.

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ebook version of He's much to blame: a comedy: in five acts. As performed at the Theatre Royal, Covent Garden. ebook version of He's much to blame: a comedy: in five acts. As performed at the Theatre Royal, Covent Garden.

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An inquiry into the Copernican system respecting the motions of the heavenly bodies, wherein it is proved, in the clearest manner, that the earth has only her diurnal motion, and that the sun revolves round the world; ... By John Cunningham An inquiry into the Copernican system respecting the motions of the heavenly bodies, wherein it is proved, in the clearest manner, that the earth has only her diurnal motion, and that the sun revolves round the world; ... By John Cunningham

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ebook version of An inquiry into the Copernican system respecting the motions of the heavenly bodies, wherein it is proved, in the clearest manner, that the earth has only her diurnal motion, and that the sun revolves round the world; ... By John Cunningham ebook version of An inquiry into the Copernican system respecting the motions of the heavenly bodies, wherein it is proved, in the clearest manner, that the earth has only her diurnal motion, and that the sun revolves round the world; ... By John Cunningham

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Evenings at home; or, the juvenile budget opened: Consisting of a variety of miscellaneous pieces, ... [pt.3] Evenings at home; or, the juvenile budget opened: Consisting of a variety of miscellaneous pieces, ... [pt.3]

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ebook version of Evenings at home; or, the juvenile budget opened: Consisting of a variety of miscellaneous pieces, ... [pt.3] ebook version of Evenings at home; or, the juvenile budget opened: Consisting of a variety of miscellaneous pieces, ... [pt.3]

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Love for love. A comedy: Acted at the Theatre in Little-Lincoln's-Inn-Fields, by His Majesty's servants. Written by Mr. Congreve. Love for love. A comedy: Acted at the Theatre in Little-Lincoln's-Inn-Fields, by His Majesty's servants. Written by Mr. Congreve.

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ebook version of Love for love. A comedy: Acted at the Theatre in Little-Lincoln's-Inn-Fields, by His Majesty's servants. Written by Mr. Congreve. ebook version of Love for love. A comedy: Acted at the Theatre in Little-Lincoln's-Inn-Fields, by His Majesty's servants. Written by Mr. Congreve.

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Nicholas Nickleby Nicholas Nickleby

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ebook version of Nicholas Nickleby ebook version of Nicholas Nickleby

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kind | kind | Unclassified | Unclassified | text | text | CC BY-SA | CC BY-SA

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Hand and heart Hand and heart

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ebook version of Hand and heart ebook version of Hand and heart

Subjects

kind | kind | Fiction -- Great Britain -- 19th century | Fiction -- Great Britain -- 19th century | Short stories -- Great Britain -- 19th century | Short stories -- Great Britain -- 19th century | text | text | CC BY-SA | CC BY-SA

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Mr. Maitland's account of inoculating the small pox Mr. Maitland's account of inoculating the small pox

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ebook version of Mr. Maitland's account of inoculating the small pox ebook version of Mr. Maitland's account of inoculating the small pox

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A letter from the Rt. Honourable Edmund Burke to His Grace the Duke of Portland: on the conduct of the minority in Parliament. Containing fifty-four articles of impeachment against the Rt. Hon. C. J. Fox. From the original copy, in the possession of the noble duke. A letter from the Rt. Honourable Edmund Burke to His Grace the Duke of Portland: on the conduct of the minority in Parliament. Containing fifty-four articles of impeachment against the Rt. Hon. C. J. Fox. From the original copy, in the possession of the noble duke.

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ebook version of A letter from the Rt. Honourable Edmund Burke to His Grace the Duke of Portland: on the conduct of the minority in Parliament. Containing fifty-four articles of impeachment against the Rt. Hon. C. J. Fox. From the original copy, in the possession of the noble duke. ebook version of A letter from the Rt. Honourable Edmund Burke to His Grace the Duke of Portland: on the conduct of the minority in Parliament. Containing fifty-four articles of impeachment against the Rt. Hon. C. J. Fox. From the original copy, in the possession of the noble duke.

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The old women weatherwise, an interlude: as performed at the Theatre Royal in Drury-Lane. The old women weatherwise, an interlude: as performed at the Theatre Royal in Drury-Lane.

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ebook version of The old women weatherwise, an interlude: as performed at the Theatre Royal in Drury-Lane. ebook version of The old women weatherwise, an interlude: as performed at the Theatre Royal in Drury-Lane.

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Sir Gawain and the Green Knight Sir Gawain and the Green Knight

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ebook version of Sir Gawain and the Green Knight ebook version of Sir Gawain and the Green Knight

Subjects

kind | kind | Gawain -- Romances | Gawain -- Romances | Poems -- England -- 14th century | Poems -- England -- 14th century | text | text | CC BY-SA | CC BY-SA

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A narrative of the method by which the private letters of Mr. Pope have been procur'd and publish'd by Edmund Curll, bookseller. NB. The original papers, in Curl's own hand, may be seen at T. Cooper's A narrative of the method by which the private letters of Mr. Pope have been procur'd and publish'd by Edmund Curll, bookseller. NB. The original papers, in Curl's own hand, may be seen at T. Cooper's

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ebook version of A narrative of the method by which the private letters of Mr. Pope have been procur'd and publish'd by Edmund Curll, bookseller. NB. The original papers, in Curl's own hand, may be seen at T. Cooper's ebook version of A narrative of the method by which the private letters of Mr. Pope have been procur'd and publish'd by Edmund Curll, bookseller. NB. The original papers, in Curl's own hand, may be seen at T. Cooper's

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An elegy to the memory of the Right Honourable William, late Earl of Bath An elegy to the memory of the Right Honourable William, late Earl of Bath

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ebook version of An elegy to the memory of the Right Honourable William, late Earl of Bath ebook version of An elegy to the memory of the Right Honourable William, late Earl of Bath

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What if the Swedes should come?: With some thoughts about keeping the army on foot, whether they come or not. What if the Swedes should come?: With some thoughts about keeping the army on foot, whether they come or not.

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ebook version of What if the Swedes should come?: With some thoughts about keeping the army on foot, whether they come or not. ebook version of What if the Swedes should come?: With some thoughts about keeping the army on foot, whether they come or not.

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An investigation of the cause of the present high price of provisions: By the author of the essay on the principle of population. An investigation of the cause of the present high price of provisions: By the author of the essay on the principle of population.

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ebook version of An investigation of the cause of the present high price of provisions: By the author of the essay on the principle of population. ebook version of An investigation of the cause of the present high price of provisions: By the author of the essay on the principle of population.

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The female Quixote: or, the adventures of Arabella. In two volumes. ... [pt.1] The female Quixote: or, the adventures of Arabella. In two volumes. ... [pt.1]

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ebook version of The female Quixote: or, the adventures of Arabella. In two volumes. ... [pt.1] ebook version of The female Quixote: or, the adventures of Arabella. In two volumes. ... [pt.1]

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Leucothoe. A dramatic poem Leucothoe. A dramatic poem

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ebook version of Leucothoe. A dramatic poem ebook version of Leucothoe. A dramatic poem

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A sermon preached at the Assizes at Durham July 29th, 1795; ... By William Paley, A sermon preached at the Assizes at Durham July 29th, 1795; ... By William Paley,

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ebook version of A sermon preached at the Assizes at Durham July 29th, 1795; ... By William Paley, ebook version of A sermon preached at the Assizes at Durham July 29th, 1795; ... By William Paley,

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Public good: being an examination into the claim of Virginia to the vacant western territory, and of the right of the United States to the same. To which is added, proposals for laying off a new state, to be applied as a fund for carrying on the war, or redeeming the national debt. By the author of Common sense. Public good: being an examination into the claim of Virginia to the vacant western territory, and of the right of the United States to the same. To which is added, proposals for laying off a new state, to be applied as a fund for carrying on the war, or redeeming the national debt. By the author of Common sense.

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ebook version of Public good: being an examination into the claim of Virginia to the vacant western territory, and of the right of the United States to the same. To which is added, proposals for laying off a new state, to be applied as a fund for carrying on the war, or redeeming the national debt. By the author of Common sense. ebook version of Public good: being an examination into the claim of Virginia to the vacant western territory, and of the right of the United States to the same. To which is added, proposals for laying off a new state, to be applied as a fund for carrying on the war, or redeeming the national debt. By the author of Common sense.

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Macbeth reconsidered; an essay: intended as an answer to part of the Remarks on some of the characters of Shakspeare Macbeth reconsidered; an essay: intended as an answer to part of the Remarks on some of the characters of Shakspeare

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ebook version of Macbeth reconsidered; an essay: intended as an answer to part of the Remarks on some of the characters of Shakspeare ebook version of Macbeth reconsidered; an essay: intended as an answer to part of the Remarks on some of the characters of Shakspeare

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The story of my boyhood and youth The story of my boyhood and youth

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ebook version of The story of my boyhood and youth ebook version of The story of my boyhood and youth

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kind | kind | Autobiographies -- United States -- 20th century | Autobiographies -- United States -- 20th century | text | text | CC BY-SA | CC BY-SA

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