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It was only in the 1960s, when Robinson introduced nonstandard analysis, that the use of infinitesimal and infinite numbers in calculus was finally placed on rigorous foundations.\n\nIn this talk, I will present some historical observations on infinitesimal numbers, and then introduce the fundamental ideas of nonstandard analysis. In the final part of the seminar, I will also show some applications of nonstandard analysis in the discrete field of combinatorics, presenting new results recently proven in arithmetic Ramsey theory, including the following: In every finite coloring (partition) of the natural numbers, one can always find a monochromatic pattern of the form a, b, a+b, b\/a.", "occurrence_notes":null, "guid":"144702-21895742@events.umich.edu", "permalink":"http:\/\/events.umich.edu\/event\/144702", "building_id":"1000166", "building_name":"East Hall", "campus_maps_id":"53", "room":"3088", "location_name":"East Hall", "has_livestream":0, "cost":"", "tags":["Mathematics"], "website":"https:\/\/umich.zoom.us\/j\/95160391122", "sponsors":[ { "group_name":"Logic Seminar - Department of Mathematics", "group_id":"4895", "website":"" }, { "group_name":"Department of Mathematics", "group_id":"3791", "website":"" } ], "image_url":"", "styled_images":{ "event_thumb":"", "event_large":"", "event_large_2x":"", "event_large_lightbox":"", "group_thumb":"", "group_thumb_square":"", "group_large":"", "group_large_lightbox":"", "event_large_crop":"", "event_list":"", "event_list_2x":"", "event_grid":"", "event_grid_2x":"", "event_feature_large":"", "event_feature_thumb":"" }, "occurrence_count":1, "first_occurrence":21895742 } , "136450-21891322": { "datetime_modified":"20260204T111402", "datetime_start":"20260220T130000", "datetime_end":"20260220T150000", "has_end_time":1, "date_start":"2026-02-20", "date_end":"2026-02-20", "time_start":"13:00:00", "time_end":"15:00:00", "time_zone":"America\/Detroit", "event_title":"LSA Opportunity Hub Pop-Up Coaching", "occurrence_title":"", "combined_title":"LSA Opportunity Hub Pop-Up Coaching", "event_subtitle":"", "event_type":"Careers \/ Jobs", "event_type_id":"2", "description":"Pop Up Coaching at the LSA Opportunity Hub presents a low stakes opportunity for students to stop by our office, grab some popcorn, and engage in a brief 10-15 minute career coaching conversation with one of our career coaches, in addition to learning about our other services and offerings! 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